Your SlideShare is downloading. ×
Mean Value Theorem
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Mean Value Theorem

3,555

Published on

Published in: Technology, Economy & Finance
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
3,555
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
28
Comments
0
Likes
1
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. 4.2 Mean Value Theorem
  • 2. Mean Value Theorem for Derivatives
    • If y = f(x) is continuous at every point of the closed interval [a,b] and differentiable at every point of its interior (a,b) then there is at least one point c in (a,b) at which
  • 3. Using Mean Value Theorem
    • Show that f(x) = 2x 2 satisfies the mean value theorem on the interval [0,2]. Then find the solution to the equation on the interval.
    • Find f’(x)
    • f’(x) = 4x
    • 4 = 4x
    • X= 1
  • 4. Using Mean Value Theorem
    • f(x) = l x – 1 l on [0, 4]
    • f(a) = -1
    • f(b) = 3
    • 1 = l x -1 l
    The function does not satisfy the mean value theorem because there is a cusp so the function is not continuous on [0,4]
  • 5. Mean Value Theorem
    • f(x) = -2x 3 + 6x – 2 , [-2 , 2]
    • f(-2) = -2(-2) 3 + 6(-2) - 2 = 2 f(2) = -2(2) 3 + 6(2) - 2 = - 6
    • f(x) = -6 - 2 = -2
    • 2 - (-2)
    • f '(x) = -6x 2 + 6
    • -2 = -6x 2 + 6
    • X = 2 -2 √3, √3
    Mean value is satisfied because the function is continuous on [-2, 2]
  • 6. Using Mean Value Theorem
    • f(x) = x 3 + 3x – 1, [0,1]
    • f(b) = 3
    • f(a) = -1
    • f’(x) = 3x 2 + 3
    • 4 = 3x 2 +3
    • X =
  • 7. Mean Value with Trig. Functions
  • 8. More mean value Solve.

×