Application of derivatives Questions and Answers

Determine whether the function is even odd or neither 43 5 x 2 f x The function fis an even function O The function fis an odd function O The function fis neither even nor odd X 5

Determine the interval s where f x 0 u 6 0 0 6 O 0 3 u 3 6 O 0 3 u 6 x x 3 is decreasing

Determine whether the function is even odd or neither k x 14x 10x The function is an even function The function is an odd function The function is neither even nor odd X

Find the points of inflection f x 8x 2x 6 O 0 2 O 2 0 O 0 6 O 6 0

Find the relative extrema of the function List your answers in terms of ordered pairs 8 x2 1 Relative maximum 0 8 No relative extrema Relative maximum 8 Relative maximum 1 8

Find where the function is concave upward 3 x 2 f x O O 2 0 O 2 None

Determine the interval s over which f x x 4 3 is concave downward O 0 4 O 4 8 O 4 0 O 8 4

Find dy dx by implicit differentiation xy 4 O 2y 02 105 2x y 0 21 X 0 1

appropriate respons Find the critical values and determine the intervals where f x is increasing and the intervals where f x is decreasing for the function f x x3 3x2 24x 6 O increasing on 4 u 2 0 decreasing on 4 O decreasing on 4 u 2 increasing on 4 2 O increasing on 4 u 2 0 decreasing on 4 2 increasing on 4 decreasing on 4 2

Find the relative extrema if any for the function f x 3x4 6x2 7 Olocal min at x 0 and local max at x 1 and x 1 Olocal max at x 1 and local min at x 0 and x 1 O local max at x 1 and local min at x 0 local max at x 0 and local min at x 1 and x 1

Find the inflection point s for f x x 7 O 3 2 6 1 O 7 0 There are no points of inflection

Graph the equation by plotting points y x To graph the equation plot at least five points Then click on the graph icon 27 24 21 18 15 12 9 6 34 3 6 9 12 15 18 21 X

15 20 Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis 15 xy 1 x 0 y 1 y 3 16 y x x 0 17 y x 2 18 x 3y 12y 9 x 0 19 x 1 y 2 x 2 y 2 y 8 x 0 4

x 63 a Find the derivative of the function and check your work by graphing both your calculated derivative and the numerical derivative of the fune 210 b Use your graph of the derivative to find points where the original function has horizontal tangent lines XV c use a graphing calculator to graph the function and indicate the points found in part b on the graph

recent poll pertaining to educational reforms involved 662 men and 840 women The margin of error is 3 5 for the male sample and 3 2 for the female sample and the level of confidence for the male portion of the poll and for the female portion of the poll HINT See Example 7 Round your answers to one decimal place ale male

For the points 9 1 and 3 5 a Find the exact distance between the points b Find the midpoint of the line segment whose endpoints are the given points Part 1 of 2 a The exact distance between the points is Part 2 of 2 b The midpoint is 0 0

2 49 Find the smallest positive angle coterminal with 3 Use radian measure A B 3TT C FI6 4TT 5 D 8TT 3

38 Find the function value to four places csc 83 40 A 1 006 B 9 065 C 0 9939 D 0 1103

43 If sine and cose 0 find csc 0 12 13 A 13 12 13 B 1920 C 13 5 D 13

TT 45 Sketch in standard position A B C D TT 3 2 2 TT 3 0 A 0 H K NA 0 0 0 TT 3 B 2 TT 3

31 Round off 5245 to three significant digits A 5300 B 5250 C 5240 D 5200

35 If cose and sine 0 find sine A 7 B 5 3 C 4 C 5

29 Given a right triangle where side a 12 and side b 16 what does angle B Give the result properly rounded off A 53 B 37 C 49 D 41

17 Find the distance between points 4 2 and 8 0 A 8 4 2 0 2 B 8 4 2 0 2 C 8 0 2 4 2 D 8 0 2 4 2 V

13 Given A B C 17 8 17 15 17 8 17 cose 15 8 17 and is in Quadrant III find sece

22 Perform the indicated operations and give the result with the proper number of significant figures 4 3 x 12 A 52 B 51 C 51 6 D 50

19 Perform the indicated operation and give the result with the proper number of significant figures 8 9 6 45 A 2 5 B 15 4 C 15 35 D 15 0

6 Use reference angles to find the value of the function cos 205 A 0 4226 B 0 4226 C 0 9063 D 0 9063

11 Givencsce 1 find sine A 1 B undefined C 0 D 1

7 Express 40 in terms of TT radians A 2 radians B 14 radians C radians 24 D radians

12 Given csc 6 1 find tane A undefined B 1 C 1

1 The angle of depression from an airplane to the landing strip of an airport is 11 The horizontal distance from the airport to a point at the base of the plane directly below the point where the angle was measured is 1300 feet How high is the airplane I A 150 feet B 1276 feet C 245 feet D 253 feet

10 If h x 2x 3 and g x X x is continuous at x 1 C I Ill only D IV only then which of the following are correct 3 I h x is not continuous at x 2 3 III hog x is not continuous at x 2 B I II only A II IV only 1 1 II g x is continuous x R IV go h x is continuous V x R C III IV only D II III only

Problem 3 Let f x y 3 a Compute the rate of change of f at the input 3 1 in the direction of the vector u 3 3 b If you take an infinitesimally small step on the surface f from the point 3 1 2 in the direction of u will you move uphill downhill or stay at the same height Justify your answer

Marcello s Pizza charges a base price of 16 for a large pizza plus 2 50 for each addit a Find a function f that models the price of a pizza with n toppings f n 16 2 50n b Find the inverse of the function f P 16 f p 2 50 What does f1 represent O f 1 represents the number of toppings on a pizza that costs 2 5 p dollars O f represents the cost of n toppings on a pizza Of 1 represents the number of toppings on a pizza that costs p dollars O f 1 represents the number of pizzas with toppings that cost p dollars Of 1 represents the cost of a pizza with n toppings c If a pizza costs 26 how many toppings does it have toppings

Consider the f x x g x x 8 Find fog x Find the domain of fog x Enter your answer using interval notation Find gof x Find the domain of gof x Enter your answer using interval notation Find f of x Find the domain of f of x Enter your answer using interval notation Find go g x Find the domain of go g x Enter your answer using interval notation

If 4x 5x xy 2 and y 2 12 find y 2 by implicit differentiation

Question 4 13pts Work out the questions from the given graph of the function f x Ay 415 10 1 2pts Determine the domain of this function 2 2pts Determine the range of this function 3 2pts Determine the intervals on which this function is increasing if any 4 2pts Determine the intervals on which this function is decreasing if any 5 1pt Determine the intervals on which this function is constant if any 6 2pts Determine the x intercepts and the y intercept of this function 7 1pt Determine the local relative maximum of f 8 1pt Determine the local relative minimum of f

Ex The cost in dollars to produce x designer dog lea x 2x 59x Find the profit function Find the number of leashes needed to be s

a Find the equation of a line passing through the point 3 5 and making an angle of 14 with the x axis Note There are two answers find them both Round values to three decimal places as needed positive slope y y b Find the equation of a line making an angle of 6 with the y axis and passing through the point 1 1 Note There are two answers find them both Round values to three decimal places as needed positive slope y negative slope y negative slope Additional Materials

The top of a dam has an angle of elevation of 1 2 radians from a point on a river Measuring the angle of elevation to the top of the dam from a point 165 feet farther downriver is 0 6 radians assume the tw angle measurements are taken at the same elevation above sea level How high is the dam Round your answer to the nearest whole number ft downriver 0 6 165 ft 1 2 a dam

Which of the following statements is not true Choose the correct answer O A The range of y csc x is 1 U 1 00 O B O C The function y csc x obtains a relative maximum at 3 2 n where n is an integer 2 x The graph of y csc x has infinitely many vertical asymptot of the form x no where n is an integer The graph of y csc x is symmetric about the y axis

When sketching the graph of y A tan Bx C D which of the following best describes how to determine the x coordinates of the halfway points of the principal cycle Choose the correct answer B A The x coordinate of the halfway points are x and x The x coordinate of each halfway point is located halfway B between the x coordinate of the center point and a vertical asymptote The x coordinate of each halfway point is located halfway O c between the x coordinate of a local maximum point and the x coordinate of a local minimum point The x coordinate of each halfway point is located halfway O D between the two vertical asymptotes E

Use Simpson s rule to approximate the value of sin xdx Use four 0 subintervals Express your answers to five decimal places b d a c 1 89612 1 92345 2 00345 2 00456

a c Evaluate sin 5x cos 4x dx cos x cos 9x 2 18 cosx cos 9x 2 FRE C 18 C 20 CELE RECHER b d cosx 2 COS X 2 cos 9x 18 cos 9x 18 C C

Write the equation x 2 2x 5 0 as a binomial squared

intercept y 2x x 4 relative minimum relative maximum point of inflection DNE Need Help x y X x y x y x y 0 0 Find the equations of the asymptotes Enter your answers as a comma Read It DNE DNE 0 0 Watch It

2 3 7 296 A building that is 225 feet tall ca angle of elevation is formed by lines fro shadow Determine the rate of change of an inverse trig function of x then take the

ct the correct choice below and fil 9x 23x 10 Factor co The trinomial is not factorable

Use the slope intercept form to graph the THE