Differentiation Questions and Answers

A company produces two types of solar panels per year x thousand of type A and y thousand of type B The revenue and cost equations in millions of dollars for the year are given as for R x y 3x 2y C x y x2 4xy 9y2 15x 72 8 Determine how many of each type of solar panel should be produced per year to maximize profit The company will achieve a maximum profit by selling solar panels of type A and selling solar panels of type B

Find the local extrema of the following function f x y 9x 4xy 4y 198x 108y 3 Find f x y and f x y f x y 18x 4y 198 fy x y 4x 8y 108 Identify the location of any local maxima Select the correct choice below and if necessary fill in the answer box to complete your ch A There are local maxima located at Type an ordered pair Use a comma to separate answers as needed B There are no local maxima

Find fxy x y if f x y x y5 7 fyy x y

What is the minimal degree Taylor polynomial about x 0 that you need to calculate sin 1 to 4 decimal places 1 degree 1 5 71 To 7 decimal places degree 1 31 1 5

9 Evaluate if possible the function a 2 b 1 c 1 d 3 e undefined f x x 12 at 11 Simplify the result

1 Find the slope of the line passing through the points 1 4 4 3 and 3 8 1 12 a 15 b 5 c 10 d 5 e 10 j

ux V 60 v 4 u 2 Determine whether u x v is directed into the screen or out of the screen Oux vis directed into the screen

Find the volume of the parallelepiped determined by the vectors a b and a 1 4 3 b 1 1 3 c 5 1 3 cubic units 34

Solve the following equation 2x 7 x 3x 2 Give your solution s to 4 decimal places

3 Find F t r2 t F t t The derivative rules may make these calculations easier

Given the following piecewise function evaluate f 2 Provide your answer below 2x f x x 2 x 2 x 1 1 x 2 2 sx

Determine the interval s for which the function shown below is increasing 6 5 3 2 10 1 2 3 16 19 in 1367S

Evaluate d dx 1 In x sin n t dt Type your answer in the space provided

If we know that S ff 1 dt t 1 3 C evaluate S f x dx

Relation f from Z to R defined by f n n 1 is a function O True False

8 Find the first order derivative of the function y x x ln x