Application of derivatives Questions and Answers

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

ing the Factor the trinomial or state that the tri 3x 13x 10 Select the correct choice below and if