Differentiation Questions and Answers

Using the figure below estimate the following 5 Round your answers to one decimal place a f g 2 b g f 2 c f f 3 d g g 3 st 3 2 g x f x 1 2 3 4 5 8

7 Evaluate the piecewise function for f 2 f x a undefined b 0 2x 5 x 2 5x2 2 x 2 c 18 d 1

44 The perimeter of a triangle is 26 inches If the longest side is twice as long as the shortest side and the third side is 2 inches longer than the shortest side If x the shortest side then two equations can be written as A z 2x and y x 2 B x 2z and x y 2 C x 2z and y x 2 D z 2x and y z 2

Find the maximum and minimum values of f x y x y subject to the curve 7x 12xy 8y 100

For those which are polynomial functions find the degree the leading term and the leading coefficient 6 f x 7x4 6x A Degree 7 leading term x4 leading coefficient 7 B Degree 4 leading term 7 leading coefficient 7x4 C Degree 2 leading term 7x4 leading coefficient 7 D Degree 4 leading term 7x4 leading coefficient 7

Let f x O O f x f x x sin a X Determine f x 2 sin a 2x cos x x3 2 sin x 2x cos x I sin x 2 x cos x sin x x x sin x x sin x

The function f is differentiable for all x values and f has exactly two critical numbers x 2 and x 5 Furthermore f 2 is a relative minimum and f 5 is a relative maximum Determine the sign positive or negative of the expression f 1 f 3 f 99 O Negative O There is not enough information to determine the sign O The value of the expression is zero O Positive A rece here claime

y tsin t y

IF you were asked to find the derivative of f x log3 x2 9x 7 it would be helpful to rewrite the expression first Which expression below is equivalent to the original expression for f x DO NOT DIFFERENTIATE 2 ln x ln 9x 7 In 3 O f x log3 x 9 logs log3 7 O In x In 9x In 7 In 3 O f x f x In 2x 9 In 3

Compute f 0 when f x 00 Write your exact numerical answer in the box below

7 8 marks Find the volume generated by revolving the region bounded by y x 4x and y 0 about a The x axis

1 60 Solve the given equation for x log X 25

Solve the right triangle shown in the figure A 52 2 c 54 a What are the lengths of the sides a Round to the nearest hundredth as needed b B C

Factor each 9 2x x 6 0 11 64x6 1 0 State the possible rational roots for each equation 13 7x 2x 7x 2 0 10 3x 22x 35 0 12 x6 64 0 14 5x 39x 27x 7

Let In 0 35xn 128 be a linear DDS a Suppose the initial value is o In 40 Find the explicit solution b Calculate the equilibrium value for this DDS Round to 2 decimal places as needed Ie c Determine the stability of the equilibrium Choose the correct answer The equilibrium of this system is Select an answer because O the slope is negative the slope in absolute value is less than 1 the slope in absolute value is greater than 1 the slope is positive

12 The number of visits to public libraries increased from 1 1 billion in 1998 to 1 3 billion in 2003 Find the average rate of change in the number of library visits from 1998 to 2003 13 Raff

Solve for x rounding to the nearest hundredth

Find the coefficient a of the given term in the expansion of the binomial Binomial Term x 9 12 ax a

7 Find the center of the ellipse 16x 9y 64x 54y 1 0 a c 2 3 2 3 b d 2 3 2 3

Find the derivative y arcsec e2x

5 5 points A rectangular poster is to contain 648 square inches of print The margins at the top and bottom of the poster are to be 2 inches and the margins on the left and right are to be 1 inch What should the dimensions of the poster be so that the least amount of poster is used

34 lim 78 n 7 A 0 n 8 The limit B does not exist O C 1 D 8

28 Find the common ratio of the geometric sequence O A B 1 6 C 213 C 6 3 1 1 18 3 2 12 72

11 Find a polynomial function with real coefficients that has these numbers as roots 4 0 3i OA x4 4x 9x 36x OB x3 4x 3x 12 C x 4x 3x 12 D x4 4x 9x 36x

16 Find the first term of this sequence an O A 113 B 1 C 610 9 D 3

The one to one function f is defined below f x 6 x Find f x where f is the inverse of f 1 f x 0

8 Let f x 3 x 5 x 3 a Determine f x BOCS b Show that the equation of the normal line to the graph of y f x at the point with an x coordinate of 7 is y 2x 11

Establish the identity Follow the format 1 sin x y sin x y 2 cos x sin y se the information given about the angle 0 to find the exact value of the indicated trigonometric function 0 3 2 a Find the exact value of cos and 0 terminates in 270 0 360 5 b Justify the choice of the sign in front of the radical given that cos 0 F

a Find the inverse of the function f x f x 7x 3 7x b What is the domain of the inverse function Enter your answer using interval notation

Use the definition of the logarithmic function to find x Simplify your answer completely a log4 x 4 X b X log10 0 01 x

Find all points where fails to be differentiable f x 13x 12 Points Note Enter points as a comma separated list with smaller a coordinates first If no solution enter NA

What is the remainder when x3 1 is divided by x x 1 O x 1 O X 02 0 0

If g x is the inverse of fx and f x 4x 12 what is g x O g x 12x 4 g x x 12 O Og x x 3 O g x x 3

7 The following table shows the values of the functions f and g and their derivatives for various values of x 0 1 2 f x 2 4 1 g x 3 1 2 f x 1 3 1 g x 3 2 0 x 3 0 2 1 1 a Let h x f x Calculate the value of h 2 g x 5 6 4 4 2 1 4 2 3 1 3 3 2 2 1 4

The traffic flow rate (cars per hour) across an intersection is r(t)=300+900t-180t², where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 8 am?

Let h be a continuous function, with its first derivative given by h '(x) = 4x³ - 10x² + e^x. Determine the interval(s) where the graph of h is concave up. (-∞, 0.431) (0.055, 1.424) (0.055, ∞) (1.424,00)

Analyze the polynomial function f(x) = 5x (x² - 9) (x + 4) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph off behaves like y = 5x^4 for large values of [x]. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)

Graph the following function using a graphing utility; then use MINIMUM to obtain the minimum value. f(x) = x² + 1/x x>0 Which graph shown below is the graph of f(x), as displayed on a graphing utility? All four graphs use the limits [0,6] by [0,30], Xscl = 1, and Yscl = 5. Find the minimum value of the function. (Round to two decimal places as needed.)

Analyze the graph of the function. x+x² +3 x²- X-64 R(x) = (a) What is the domain of R(x)? OA. {x|x #0} B. (xlx #8 and x# - 8} C. (xlx #0 and x#8 and x# - 8} D. All real numbers (b) What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. OA. X= (Use a comma to separate answers as needed. Type an integer or a fraction.) B. There is no vertical asymptote.

Find bounds on the real zeros of the polynomial function. f(x)=x²-24x² - 25 The lower bound is and the upper bound is (Type integers or simplified fractions.)

A company finds that if they price their product at $ 40, they can sell 372 items of it. For every dollar increase in the price, the number of items sold will decrease by 6. What is the maximum revenue possible in this situation? A dollars. What price will guarantee the maximum revenue?

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. (Enter your answer using interval notation. Round your answer to four decimal places.) cee f(x) = e* = 1 + x +. 21 x<0

What are the solutions of the equation sin x cot x = - 2 Drag all correct solutions to the box to correctly complete the table. Solutions to sin cot x = 2 - √2 2 on the interval on the interval [0, 2π), [0, 2TT)

A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units 7π The graph of the function does not show a phase shift. 12 down, and the period of the function is What is the equation of the cosine function described? Drag a value into each box to correctly complete the equation of the function. f(x) = cos( x)

Consider the series + + + 27 +31 +.... Does the series converge or diverge? Select answers from the drop-down menus to correctly complete the statements. The series Choose... You conclude this because the series is

The polar equation r = 7 sin What is the length of the petals of this rose? Enter your answer in the box.

A bank pays continuous compounded interest. Sue deposits $100 in the account, and in 5 years she has $120. Write and solve the differential equation for A(t), the amount of money in Sue's account at time t. O A(t) = 1.2e(0.035)t O A(t) = 100e(-0.035)t O A(t) = 100e (1.2) o A(t)= =100e (0.035)t

Given that the polynomial function has the given zero, find the other zeros. f(x) = x³ + 4x² - 6x - 24; - 4 The other zero(s) is/are___ (Type exact answers, using radicals as needed. Use a comma to separate answers as needed.)

Samuel invested $9,200 in an account paying an interest rate of 7% compounded monthly. Noah invested $9,200 in an account paying an interest rate of 73/% compounded daily. After 7 years, how much more money would Noah have in his account than Samuel, to the nearest dollar?

An object's velocity after t seconds is v() = 36 - 21 feet per second. (a) How many seconds does it take for the object to come to a stop (velocity=0)? ___seconds (b) How far does the car travel during that time?____ feet (c) How many seconds does it take the car to travel half the distance in part (b)?______ seconds