Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this document? Why not share!

- Community Mapping Capacity - Elderl... by ChyldeofFire 507 views
- Purchase Habits of people 35 years ... by Davide Fanesi 490 views
- Sochi olympics worksheet by MrsJudd 201 views
- презентация к лаб.раб. 1 by student_kai 195 views
- HarvardMUN India '14 - Al Jazeera: ... by Chanakya Varma 987 views
- Total parenteral nutrition 2 by Venkatesh Kolla 748 views

No Downloads

Total views

594

On SlideShare

0

From Embeds

0

Number of Embeds

2

Shares

0

Downloads

4

Comments

0

Likes

1

No notes for slide

- 1. Name: xxxxxxxxxxxxxxx ID: xxxxxxxxxxx Class: xxxx INDIVIDUAL ASSIGNMENT 1. The balance of a bank account after 3 years with respect to the interest rate r% is given by A= 1000(1+r/1000)36 Find the rate of change of the balance with respect to r when r = 6 SOLUTION A=1000(1+6/1000) =1000(1+0.006) 36 36 = 1000(1.24) =1240.3 36= 3 YEARS 12= 1 YEAR A=1000(1+6/1000) 12 =1074.42 AVERAGE RATE OF CHANGE IS GIVEN BY: Y3-Y1/X3-X1 1240.3-1074.42/36-12 ARC = 6.912 2- Find f (a) for given value of a. f(x) = 5x2- 4x + 7; and a = 4: SOLUTION 2 F(x) =5x -4x+7 F’(x) =10x-4
- 2. F’ (4) =10(4)-4 F’ (a) =36 3- Find f (g(x)) and g (f(x)) for f(x) = 4x + 3; and g(x) = -2x + 1: SOLUTION F (G(X)) = f (-2x+1) = 4(-2x+1) +3 = -8x+7 G (f(x)) = g (4x+3) = -2(4x+3) +1 =-8x-5 4- Let s be a distance given by S (t) = 3t3 + 4t2 + 8t: Find the acceleration. SOLUTION 3 2 S (t) = 3t +4t +8t To find the acceleration we derive the function twice 2 S’ (t) = 9t +8t S’’ (t) = 18t+8 5- Find f0(x) for f(x) = 10/x Solution 6 F (x) = 10/x =10x -6 6
- 3. F’ (x) = -60x -7 6- For the function f(x) = 5x2 + 4x. Find f(x + h) - f(x)/h For: a. x = 2; h = 0:1. b. x = 1; h = 0:5. c. x = 3; h = 1. Solution 2 a- f (2) =5(2) +4(2) =28 2 F (2+0.1) = 5(2+0.1) +4(2+0.1) =30.09 30.09-28/0.1=20.9 b- F (1) =5(1) +4(1) =9 2 F (1+0.5) =f (1.5) +4(1.5) =17.25 17.25-9/0.5=16.5 2 c- F (3) =5(3) +4(3) =57 2 F (3+1) =5(3+1) +4(3+1) =96 96-57/1=39 7- Find the limit if it exists lim 10x+3 X 3 Lim 10x+3 = lim 10x+3 = 33 + x 3 x 3 3 8- Differentiate the function y = 5x (2x - 7x)
- 4. SOLUTION). USING CHAIN RULE: F(X).G(X) = F’(X).G(X) + G’(X).F(X) F(X) =5X F’(X) =5 3 2 G’(X) = 6X -7 G(X) =2X -7X 3 2 Y’= 5. (2x -7x)+ (6x -7)5x 3 Y’= 4x -7x 2 9- Differentiate the function y= 2x/x +4 F(x) =2x f’(x) =2 2 G(x) =x +4 g’(x) = 2x Y’ = g(x).f’(x)-f(x).g’(x)/g(x) 2 2 2 Y’ = (x +4).2 – 2x (2x) / (x +4) 2 2 Y’ = -2(x +8) / (x +4) 2 2 10- Find an expression for dy/dx: y = 3u2 and u = 3x + 1: Dy/du= 6u, and du/dx= 3 Dy/dx= dy/du.U + du/dx.y 2 = 6u. (3x + 1) + 3. (3u ) = 18ux + 6u + 9u 2 2 = 3u + 6ux + 2u 3 2 12- Find the absolute maximum and minimum of the function f(x) = 2x - 3x + 4 on the interval [-1; 2]. SOLUTION
- 5. 2 F’(x) = 6x -6x F’(x) =0 2 6x -6x =0 6x(x-1) =0 6x=0 or x-1=0 X=0, X=1 {-1, 0, 1, 2} F (-1) =-1 F (0) =4 F (1) =3 F (2) =8 The absolute maximum is 8= f (2) The absolute minimum is -1= f (-1) 3 13- Find dy for given values of x and dx: y = x ; Dy/dx=3x 2 x = 4 and dx = 0:1 2 dy= 3x .dx Dy= 3(4). (0.1) Dy=4.8 3 14- Determine where the function is concave up and down: f(x) = x - 3x + 2: Concavity can be found using the second derivative. 2 F’ (x) = 3x -3 F’’(x) = 6x -to find where the function is concave up, we find where the second derivative is positive 6x>0 x>0: the function is concave up for all x- values > 0. Similarly, the function is concave down for all x-values < 0.
- 6. 3 2 16- The cost of producing x items is given by: C(x) = x -34x + 5600x: Find the production level that minimizes the average cost. 3 C(x)/x 2 2 x -34x +5600x/x = x -34x+5600 3 2 3 17- Find dy=dx by implicit differentiation, given that x + xy + y = 3: 3 2 3 D/dx(x +xy +y ) =d/dx (3) 3 2 3 D/dx(x ) +d/dx (xy ) +d/dx (y ) =0 2 2 2 3x +x.2y.dy/dx+y +3y d/dx=0 2 2 2 2 2 3y d/dx+2yxdy/dx=-3x -y 2 (3y +2yx) dy/dx=-3x -y 2 2 2 Dy/dx= -3x -y /3y +2yx Find the slope of the tangent line at point (1; 1). y - y0 = m(x - x0) 18- The cost and the revenue with respect to the number of items is given by C(x) = 200x + 2000 and 2 R(x) = 5x + 100x + 80: Find the marginal profit Solution P(X) = R(x) – C(x) 2 P(x) = (5x +100x+80) – (200x +200) 2 P(x) = 5x – 100x -120 P’(x) = 10x-100

No public clipboards found for this slide

Be the first to comment