SlideShare a Scribd company logo
1 of 1
Download to read offline
suppose that the continous function f: R2 to R has a tangent plane at the point (x1,y1,f(x1,y1)).
prove that the function f: R2 to R has a directional derivative in all direction at point (x1,y1)
Solution
The function is z = f(x,y)
The tangent plane will have equation as
Z-f(x1,y1) = fx (x-x1) +fy(y-y1)
Thus fx, fy are the derivatives (partial of f)
Directional derivative along the point (x1,y1) is
fx (x-x1)+fy(y-y1)
Thus proved

More Related Content

More from arihanthtoysandgifts

Identify the unique characteristics of auditing professionSoluti.pdf
Identify the unique characteristics of auditing professionSoluti.pdfIdentify the unique characteristics of auditing professionSoluti.pdf
Identify the unique characteristics of auditing professionSoluti.pdf
arihanthtoysandgifts
 
Explain the purpose of the Medium Access Control (MAC) timing paramet.pdf
Explain the purpose of the Medium Access Control (MAC) timing paramet.pdfExplain the purpose of the Medium Access Control (MAC) timing paramet.pdf
Explain the purpose of the Medium Access Control (MAC) timing paramet.pdf
arihanthtoysandgifts
 
Describe the arrangement of neurons in the primary motor cortexS.pdf
Describe the arrangement of neurons in the primary motor cortexS.pdfDescribe the arrangement of neurons in the primary motor cortexS.pdf
Describe the arrangement of neurons in the primary motor cortexS.pdf
arihanthtoysandgifts
 
A case study of a young man with a viral infection In the late winte.pdf
A case study of a young man with a viral infection  In the late winte.pdfA case study of a young man with a viral infection  In the late winte.pdf
A case study of a young man with a viral infection In the late winte.pdf
arihanthtoysandgifts
 
Write the program in MIPS that declares an array of positive integer.pdf
Write the program in MIPS that declares an array of positive integer.pdfWrite the program in MIPS that declares an array of positive integer.pdf
Write the program in MIPS that declares an array of positive integer.pdf
arihanthtoysandgifts
 
Why does a diploid mother cell that undergoes meiosis produce four h.pdf
Why does a diploid mother cell that undergoes meiosis produce four h.pdfWhy does a diploid mother cell that undergoes meiosis produce four h.pdf
Why does a diploid mother cell that undergoes meiosis produce four h.pdf
arihanthtoysandgifts
 
What is an intumescent material Where is it used SolutionAn .pdf
What is an intumescent material Where is it used  SolutionAn .pdfWhat is an intumescent material Where is it used  SolutionAn .pdf
What is an intumescent material Where is it used SolutionAn .pdf
arihanthtoysandgifts
 
1. How can a computer with only 2G of physical memory run two progra.pdf
1. How can a computer with only 2G of physical memory run two progra.pdf1. How can a computer with only 2G of physical memory run two progra.pdf
1. How can a computer with only 2G of physical memory run two progra.pdf
arihanthtoysandgifts
 

More from arihanthtoysandgifts (20)

How do humans detect color Considering your answer to this question.pdf
How do humans detect color Considering your answer to this question.pdfHow do humans detect color Considering your answer to this question.pdf
How do humans detect color Considering your answer to this question.pdf
 
Identify the unique characteristics of auditing professionSoluti.pdf
Identify the unique characteristics of auditing professionSoluti.pdfIdentify the unique characteristics of auditing professionSoluti.pdf
Identify the unique characteristics of auditing professionSoluti.pdf
 
Hemophilia is a recessive trait. The dominant trait is normal blood d.pdf
Hemophilia is a recessive trait. The dominant trait is normal blood d.pdfHemophilia is a recessive trait. The dominant trait is normal blood d.pdf
Hemophilia is a recessive trait. The dominant trait is normal blood d.pdf
 
Explain the purpose of the Medium Access Control (MAC) timing paramet.pdf
Explain the purpose of the Medium Access Control (MAC) timing paramet.pdfExplain the purpose of the Medium Access Control (MAC) timing paramet.pdf
Explain the purpose of the Medium Access Control (MAC) timing paramet.pdf
 
find the payment necessary to amortize 8 loan of $1500 for 19 compo.pdf
find the payment necessary to amortize 8 loan of $1500 for 19 compo.pdffind the payment necessary to amortize 8 loan of $1500 for 19 compo.pdf
find the payment necessary to amortize 8 loan of $1500 for 19 compo.pdf
 
explain why HCO3- levels can be calculated from pH and pCO2 levels.pdf
explain why HCO3- levels can be calculated from pH and pCO2 levels.pdfexplain why HCO3- levels can be calculated from pH and pCO2 levels.pdf
explain why HCO3- levels can be calculated from pH and pCO2 levels.pdf
 
Describe the arrangement of neurons in the primary motor cortexS.pdf
Describe the arrangement of neurons in the primary motor cortexS.pdfDescribe the arrangement of neurons in the primary motor cortexS.pdf
Describe the arrangement of neurons in the primary motor cortexS.pdf
 
Cell Image Cell type eukaryotic cell t prokaryotic cell Solution.pdf
Cell Image Cell type eukaryotic cell t prokaryotic cell Solution.pdfCell Image Cell type eukaryotic cell t prokaryotic cell Solution.pdf
Cell Image Cell type eukaryotic cell t prokaryotic cell Solution.pdf
 
An inbred line of Drosophila will drink sugar water to which small am.pdf
An inbred line of Drosophila will drink sugar water to which small am.pdfAn inbred line of Drosophila will drink sugar water to which small am.pdf
An inbred line of Drosophila will drink sugar water to which small am.pdf
 
ACC312 Federal TaxationTax avoidanceTax evasion questions1. The.pdf
ACC312 Federal TaxationTax avoidanceTax evasion questions1. The.pdfACC312 Federal TaxationTax avoidanceTax evasion questions1. The.pdf
ACC312 Federal TaxationTax avoidanceTax evasion questions1. The.pdf
 
a total of 100 students are taking a history exam. each student is r.pdf
a total of 100 students are taking a history exam. each student is r.pdfa total of 100 students are taking a history exam. each student is r.pdf
a total of 100 students are taking a history exam. each student is r.pdf
 
A case study of a young man with a viral infection In the late winte.pdf
A case study of a young man with a viral infection  In the late winte.pdfA case study of a young man with a viral infection  In the late winte.pdf
A case study of a young man with a viral infection In the late winte.pdf
 
A child drops a ball from a bridge. The ball strikes the water under.pdf
A child drops a ball from a bridge. The ball strikes the water under.pdfA child drops a ball from a bridge. The ball strikes the water under.pdf
A child drops a ball from a bridge. The ball strikes the water under.pdf
 
2. A resistant inbred cultivar and a susceptible inbred cultivar are.pdf
2. A resistant inbred cultivar and a susceptible inbred cultivar are.pdf2. A resistant inbred cultivar and a susceptible inbred cultivar are.pdf
2. A resistant inbred cultivar and a susceptible inbred cultivar are.pdf
 
Write the program in MIPS that declares an array of positive integer.pdf
Write the program in MIPS that declares an array of positive integer.pdfWrite the program in MIPS that declares an array of positive integer.pdf
Write the program in MIPS that declares an array of positive integer.pdf
 
Why does a diploid mother cell that undergoes meiosis produce four h.pdf
Why does a diploid mother cell that undergoes meiosis produce four h.pdfWhy does a diploid mother cell that undergoes meiosis produce four h.pdf
Why does a diploid mother cell that undergoes meiosis produce four h.pdf
 
What is an intumescent material Where is it used SolutionAn .pdf
What is an intumescent material Where is it used  SolutionAn .pdfWhat is an intumescent material Where is it used  SolutionAn .pdf
What is an intumescent material Where is it used SolutionAn .pdf
 
1. How can a computer with only 2G of physical memory run two progra.pdf
1. How can a computer with only 2G of physical memory run two progra.pdf1. How can a computer with only 2G of physical memory run two progra.pdf
1. How can a computer with only 2G of physical memory run two progra.pdf
 
this is VerilogHDL classAre these legal identifiersa. system1.pdf
this is VerilogHDL classAre these legal identifiersa. system1.pdfthis is VerilogHDL classAre these legal identifiersa. system1.pdf
this is VerilogHDL classAre these legal identifiersa. system1.pdf
 
Transactions made by Ivanhoe Company for the month of March are shown.pdf
Transactions made by Ivanhoe Company for the month of March are shown.pdfTransactions made by Ivanhoe Company for the month of March are shown.pdf
Transactions made by Ivanhoe Company for the month of March are shown.pdf
 

Recently uploaded

Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPSSpellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
AnaAcapella
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
中 央社
 
Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...
Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...
Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...
EADTU
 

Recently uploaded (20)

Improved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio AppImproved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio App
 
PSYPACT- Practicing Over State Lines May 2024.pptx
PSYPACT- Practicing Over State Lines May 2024.pptxPSYPACT- Practicing Over State Lines May 2024.pptx
PSYPACT- Practicing Over State Lines May 2024.pptx
 
When Quality Assurance Meets Innovation in Higher Education - Report launch w...
When Quality Assurance Meets Innovation in Higher Education - Report launch w...When Quality Assurance Meets Innovation in Higher Education - Report launch w...
When Quality Assurance Meets Innovation in Higher Education - Report launch w...
 
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdfFICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
 
How to Manage Website in Odoo 17 Studio App.pptx
How to Manage Website in Odoo 17 Studio App.pptxHow to Manage Website in Odoo 17 Studio App.pptx
How to Manage Website in Odoo 17 Studio App.pptx
 
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPSSpellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
 
The Story of Village Palampur Class 9 Free Study Material PDF
The Story of Village Palampur Class 9 Free Study Material PDFThe Story of Village Palampur Class 9 Free Study Material PDF
The Story of Village Palampur Class 9 Free Study Material PDF
 
8 Tips for Effective Working Capital Management
8 Tips for Effective Working Capital Management8 Tips for Effective Working Capital Management
8 Tips for Effective Working Capital Management
 
An Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge AppAn Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge App
 
Including Mental Health Support in Project Delivery, 14 May.pdf
Including Mental Health Support in Project Delivery, 14 May.pdfIncluding Mental Health Support in Project Delivery, 14 May.pdf
Including Mental Health Support in Project Delivery, 14 May.pdf
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
 
Major project report on Tata Motors and its marketing strategies
Major project report on Tata Motors and its marketing strategiesMajor project report on Tata Motors and its marketing strategies
Major project report on Tata Motors and its marketing strategies
 
An overview of the various scriptures in Hinduism
An overview of the various scriptures in HinduismAn overview of the various scriptures in Hinduism
An overview of the various scriptures in Hinduism
 
ESSENTIAL of (CS/IT/IS) class 07 (Networks)
ESSENTIAL of (CS/IT/IS) class 07 (Networks)ESSENTIAL of (CS/IT/IS) class 07 (Networks)
ESSENTIAL of (CS/IT/IS) class 07 (Networks)
 
AIM of Education-Teachers Training-2024.ppt
AIM of Education-Teachers Training-2024.pptAIM of Education-Teachers Training-2024.ppt
AIM of Education-Teachers Training-2024.ppt
 
UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024
 
Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...
Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...
Transparency, Recognition and the role of eSealing - Ildiko Mazar and Koen No...
 
ANTI PARKISON DRUGS.pptx
ANTI         PARKISON          DRUGS.pptxANTI         PARKISON          DRUGS.pptx
ANTI PARKISON DRUGS.pptx
 
Đề tieng anh thpt 2024 danh cho cac ban hoc sinh
Đề tieng anh thpt 2024 danh cho cac ban hoc sinhĐề tieng anh thpt 2024 danh cho cac ban hoc sinh
Đề tieng anh thpt 2024 danh cho cac ban hoc sinh
 

suppose that the continous function f R2 to R has a tangent plane a.pdf

  • 1. suppose that the continous function f: R2 to R has a tangent plane at the point (x1,y1,f(x1,y1)). prove that the function f: R2 to R has a directional derivative in all direction at point (x1,y1) Solution The function is z = f(x,y) The tangent plane will have equation as Z-f(x1,y1) = fx (x-x1) +fy(y-y1) Thus fx, fy are the derivatives (partial of f) Directional derivative along the point (x1,y1) is fx (x-x1)+fy(y-y1) Thus proved