Differentiation Questions and Answers

Compute the derivative of f x x sin x Use the result to compute f AT 1 B 2 C 3 D 4

Tutorial Exercise Analyze and sketch a graph of the function Label any intercepts relative extrema points of inflection and asymptotes x28x 37 X 6 y Step 1 Begin by finding the intercepts If an answer does not exist enter DNE To find the y intercept substitute x 0 and solve for y The y intercept is 37 6 To find the x intercept substitute y 0 and solve for x Step 2 x y 0 The x intercept is 37 6 x y DNE y Next differentiate the given function y 2x8 x6 x 6 0 x 1 x 11 x 6 DNE x 8x 37 and write as a single fraction completely factored x 6 x 8x 37 x 6

n Find the value V of the Riemann sum V f ck Axk k 1 for the function f x x 3 using the partition P 0 2 4 7 where c is the right endpoint of the partition

Find the derivative of the function f x 3x 4 f x 2 3 3x 4

integral fesz Use a Table of Integrals to evaluate the integral sin 6xdx

Find dy by implicit differentiation II y cos x 5x 2y

Differentiate the function y y 6e 1 8 18e x 5 3x S 5 x 3

Find f x and f x f x f x f x X 2 3

Find the number e that satisfies the conclusion of the Mean Value Theorem on the given interval Enter your answers as a comma separated list If an answer does not exist enter DNE f x x 0 4 CH Graph the function the secant line through the endpoints and the tangent line at c f c y y 3 0 2 5 2 0 1 5 1 0 0 5 3 0 5 1 0 1 5 2 0 Are the secant line and the tangent line parallel Yes 3 2 5 3 0 3 0 2 5 2 0 1 5 1 0 0 5 N 0 5 M 3 N 1 0 1 5 20 2 5 3 0

T IOSA and the area under the curvey cosx from x k to x A 1 471 A OB OC B 1 414 C 1 277 D 1 120 is 0 1 then E 0 436

Use the graph of y f x to answer the following 6 5 4 3 2 9 5 y f x 3 e POR 2 2 3 4 54 T 2 3 4 5 6

1 A manufacturing company performs a quality control analysis on the ceramic tile it produces Suppose a batch of 23 tiles has 8 defective tiles If 6 tles are sampled at random what is the probability that exactly 1 of the sampled tiles is def How many ways can 6 tiles be selected from 23 tiles ways Type a whole number The probability that exactly 1 of the sampled tiles is defective is Round to four decimal places as needed

The equation of motion of a particle is s t4 3t t t where s is in meters and t is in seconds Assume t 0 a Find the velocity v t and acceleration a t as functions of t v t a t b Find the acceleration in m s after 1 1 s a 1 1 m s c Graph the position velocity and acceleration functions on the same screen 2 2 0 5 1 0 S 1 5 a 2 0 2 5 3 0 X WH a 0 5 1 0 1 5 2 0 2 5 2 2 3 0 X

Let y x x 8 x 5 Solution y Use the Quotient Rule to find y x 5 x 5 x 5 d dx x 5 x x 8 x 5 x x 8 x 5 x 5 d

Differentiate f x f x 4 sin x 5 cos x

Differentiate the function y y 2ex 7 x X

dw or the given functions a express as a function of t both by using the Chain Rule and by expressing wi dt erms of t and differentiating directly with respect to t Then b evaluate w 10x 2y x cos t y sint t 4 a Express dw dt 11 dw dt 3x as a function of t dw dt at the given value of t

Decide whether or not the matrices A and B are inverses of each other 1 A 3 42 Inverses O Not Inverses B 11 2 2

Decide whether the statement is true or false 4 5 6 7 4 5 Edit View Insert Format Tools Table 12pt Paragraph T

Write the solution from the final simplex table X2 1 2 Z 13 0 0 1 0 X1 0 2 0 0 1 010 24 16 1 200 O x 0 X2 24 S 0 2 16 z 200 O x1 0 x2 16 S 0 24 z 200 O x 2 X2 24 S 0 16 z 200 O x 24 x 16 S 0 S2 0 z 200

a Let f x sin x Find f x f x b Let f x sin 2 Find f x f x

If possible find the location of an obsulate extrem J of the function on the interval given g x 2x 3x 120 x 8 0 6 select the correct choice below if necessary fill in the anny has an absolute maximum at x A The function gly inimimm at x aun B The function gox has no absolote maximum and at x absolute minimum The functiun x and X g x has an obsolute maximum at absolute minimum pal the function g x does not have an absolute maximum or an absolute minimum

10 find dy by implict diftention dy to 10000440 2xy y 1 Toption A Y 9 x By Z G Mund all 7 0 y wwwxx Nive 50 50 5002001

Find two linearly independent solutions of y 8xy 0 of the form y 1 a3x a6x6 y2 x b x b7x Enter the first few coefficients a3 a6 b4 b b7 help numbers help numbers help numbers help numbers

2 Assume x and y are function of Evaluate dyldt Xy x 12 dx 3 x 2 Y 5 pl option A g B 34 P c 9

y find dy g 24 14 at 20 at the given point 7 xe y

Use the given graph of f x 1 x to find a number 8 such that if x2 6 then 0 5 0 2 8 1 07 as 03 0 X x 1 2 10 2 T 10 J x

Calculate two iterations of Newton s Method to approximate a zero of the function using the given initial guess Round you answers to four decimal places f x cos x X 0 5 n 1 2 Xn f xn 0 6886 f x 0 4794 X 0 72504 X f x f xn 1 830 0 950 Xn 2 330 3 280 f xn f xn X X

m When you have taken your notes type the domain of the graph shown below in interval notation into the text box and then click Submit Assignment Reminder if the graph runs to the edge of the graph paper then you should assume it keeps going in along the same trajectory forever 8 6 4 2 A 6 4 2 2 2 4

Which of the following pairs of graphs could represent the graph of a function and the graph of its derivative A I only B II only C III only OD I and III OE II and III 11 K K f 111 bk

6 Acm 1 3cm 8 2cm 5cm 7 3 5cm 4 7cm 8 2cm C 7cm lo 3cm 85cm 104cm 3 5cm

Use the graph of f to find the largest open interval on which f is increasing and the largest open interval on which f is decreasing Enter your answers using interval notation y 10 8 6 ip 2 2 8 10 X a Find the largest open interval s on which f is increasing Enter your answer as a comma separated list of intervals b Find the largest open interval on which f is decreasing

Use the basic rule for differentiation to obtain the derivative of the following function 1 f x 3x5 4x 1 2 f x 2 x x w 513 1 P

Let g x 8 x 8 x 8 Use logarithmic differentiation to determine the derivative of g

Question 2 Below is the function f x 6 5 74 5 4 O 1 O 1 O xx 26 4 24 3 7 3 4 Over which interval of x values is f 0 O 1 00 O 1 00 O 1 O 1 O 0 00 Over which interval of x values is 0 0 1 00 O 1 00 6 Over the interval 0 o this function is

For the following exercises find 21 22 in polar form 23 1 2 3 cis 116 2 cis 82 24 1 2 cis 205 22 2 2 cis 118

Find the slope of the tangent line to the graph at the given point 4x y2 x 2 2 Cissoid 31 y 2 0 2 3 2 XN 2 2

This question asks for an algebraic expression With these types of questions be sure to use the variables indicated In your answer you can also use mathematical expressions for numerical calculations Examples Type 3x 2 5 2 x 3 X 2 x 3 x sqrt x 5 x 5 3 x 7 32 7 1 x x 1 2 3 1 x x 1 5 3x 2 3 To get 3x 5 1 Enter 5 3 x On the square root be sure to put parentheses around the input sqrt x 3 is OK but sqrtx 3 or sqrt x 3 is not Unless the problem gives specific directions any algebraically equivalent expressions acceptable For example if the answer was x 2 x 3 then x 3 x 2 and 3 x 2 x would also be acceptable Try it here Use the Preview button to see how the computer is interpreting what you typed x 4 x 1 5 2 below

y values 9 8 7 6 5 4 3 2 1 If f x g x 1 g x h x 2 3 x values then 4 f 3 Question Help Message instructor out y values 5 4 3 2 1 h x 1 2 3 x values 4

The limit represents the derivative of some function Fat some number a State such an fand a lim 8 IT 7 sin 8 Of x sin x a Of x sin x a Of x cos x a Of x sin x a Of x cos x a TT S 77 4 T J 3 Of x cos x a

The graph of a function h is shown below Find h 4 3 2 1 3 4 1 2 3 4 5 6 2 3 5 6 h 4 0

Find the partial derivatives of the function This material is review and a warm up from chapter 12 3 f x y f x y fay x y P f x y zye

A graphing calculator is recommended Let y 14 1 e a Find an equation of the tangent line to the curve y at the point 0 7 b Illustrate part a by graphing the curve and the tangent line on the same screen y 0 3 10 5 0 7 2 1 10 0 7 1 2 3 1 10 0 7 10

For the given composite function identify the inner function u g x and the outer function y f u Use non identity functions for f u and g x y tan xx fu g x Find the derivative 618 11

nd the linear function with the following properties nswer f 3 7 f 2 12

Find a formula for the linear function depicted in the following graph Answer 10 5 Enable Zoom Pan 10 X

A pet store has 6 cats Here are their weights in pounds 11 12 13 7 10 5 Find the mean weight of these cats If necessary round your answer to the nearest tenth pounds X

On a survey 8 students reported how many minutes it takes them to travel to school Here are their responses 8 6 4 8 14 10 8 3 Find the mean travel time for these students If necessary round your answer to the nearest tenth minutes X 5

Ax If y 2dc then find dy dx Sx OA 71x OB 63x OC 7x OD 26x O E 99x

THE TOP AND BOTTOM MARGINS OF A PAGE ARE BOTH 1 cm AND THE SIDE MARGINS ARE EACH 1cm IF THE AREA OF THE PRINTED MATERIAL PER PAGE IS FIXED AT 30cm2 WHAT ARE THE DIMENSIONS OF THE PAGE OF LEAST AREA