Differentiation Questions and Answers

Solve the following equation for x Answer as a fraction simplified in lowest terms Provide your answer below 2x 7 3 3 2

Find the slope of the following line Give your answer as a single number y 6x 1

Find the y intercept of the following line Give your answer as an ordered pair a b y x 2

Find the sum S of the geometric sequence that satisfies the stated conditions 2 7 1 r 2 n 8 X Sn 510

For this weekly quiz you will show that given f g are continuous f g x 10 4 4 x 3 and then lim I 3 lim T 3 g x 7 x 3 8 f 7 2 To earn full credit you should clearly show your steps and justify your steps example if you are using limit laws then say how you are using it

Find the value of the derivative for the given function dr dr de 0 0 if r 7 16 0 Type an integer or a simplified fraction

The slope of the tangent to the curve f x 32 3 at x 2 is O O 1 9 1 3 19 1

Evaluate the following limit lim 2 x 2 x 2 does not exist 0 4 undefined

2 A typical soda can contains 355 ml of soda Determine the dimensions that a soda can Recall that 1 ml 1 cubic will minimize the cost of manufacturing centimeter Coca Co

Find the area of the parallelogram whose vertices are given below A 1 2 B 3 0 C 7 3 D 3 5 The area of parallelogram ABCD is square units Type an exact answer using radicals as needed

Find the component form of the unit vector obtained by rotating the vector 1 0 210 counterclockwise about the origin Choose the correct answer below OA 2 2 2 2 O C O E 12 0 1 3 2 2 2 3 2 www OB 3 2 OD 2 2 O F 2 2 2

Describe the given set with a single equation or with a pair of equations The plane through the point 2 7 1 parallel to a the xy plane b the yz plane c the xz plane BILLED a Choose the correct equation of a plane parallel to the xy plane O A y 7 B z 1 OC x 2

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

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

Tutorial Exercise Find the derivative of the function 4x 6x f x Step 1 The function f x can be simplified to make the algebraic process of finding the derivative easier f x 4 6

Find the given higher order derivative f 3 x x8 f 4 x f 4 x x x8 f x Your answer cannot be understood or graded More In

Function f x tan x Point a Find an equation of the tangent line to the graph of the function at the given point Let x be the independent variable and y be the dependent variable b Use a graphing utility to graph the function and its tangent line at the point y R A KIN C YX AUX O O A

The tangent line to the graph of y g x at the point 5 2 passes through the point 8 6 Find g 5 and g g 5 g 5

a f 0 b f 1 c f 2 d f 3 e f 4 f f 5 g f 6 h f 7 YA 1 0 1 y f x X

y I Show Transcribed Text 2 RISE rea of the inscribes polygon or circumscribed indicated

Simplify the following rational expression Give your answer as a reduced rational expression x 2x 3 x 1

Express the following with rational exponents

Find all the second order partial derivatives of the following function W 4x 2y 2 2x 2y

7e7x e7x 2 This can be transformed into a basic integral by letting Consider the indefinite integral u du and du Te dx Performing the substitution yields the integral da

f x 3x 8 Find the inverse of f x O A f x 3x 8 OB f x 28 O c f x 3 OD f x 8 3x

Write the following expression in simplified radical form 128 12 10 z Assume that all of the variables in the expression represent positive real number

Step 3 of 3 Are the following functions Inverses of one another Answer 2 Points f x x 5 and g x x 4 Yes No

Write the expression as a single logarithm 1 3 log2y log w 5log z 4

q x Step 2 of 4 Identify the shape of the more basic function found in step 1 Answer 2 Points x x 3 Ay X X Ke

Consider the following function g x Step 1 of 4 Determine the more basic function that has been shifted reflected stretched or compressed Answer 2 Points x 1 f x

Evaluate the determinant of the matrix A 30 9 10 23

Write a formula for the function g x described as follows Use the function f x Answer 2 Points x2 Move the function to the right by 3 units and up by 1 unit

Simplify the following assuming x 0 y 0 and z 0 338x6y z 288x6y z

Simplify assuming that x 0 and y 0 112x32y25 7x6y

The following formula gives the total surface area S of a cylinder with radius r and height h S 2 r r h Find the total surface area of a cylinder with radius 9 and height 7 Provide your answer below

Solve the initial value dx t 12t 32 1 t 8 x 9 0 dt problem for x as a function of t

If F x tan 1 dt find all ritical numbers of F in the interval 3 3 Type your answer in the space provided and show your work that is show how you found your answers 0 For the toolbar press ALT F10 PC or ALT FN F10 Mac