Differentiation Questions and Answers

and Proof K Question 5 GA 3 18 Part of 6 Write the converse inverse and contrapositive of the s If a statement is false give a counterexample If I am in Mississippi then I am in the South Write the converse of the conditional Choose the cor A If I am in the South then I am in Mississippi OB If I am not in Mississippi then I am not in the

f Find f g f g fg and and their domains Enter your answers for all domains in interval notation 9 f g x domain f g x domain fg x domain 1 x domain f x g x 11 11 11 3 x 3

w many songs can a digital music player hold The data below represent the memory x and the number of songs mplete parts a through f below Memory x Number of Songs gigabytes 4 8 16 32 2050 4100 8200 16400 Question 17 4 1 51 Part 7 of 10 Plot the ordered pairs x h in a Cartesian plane Choose the correct graph on the right Show that the number of songs n is a linear function of the memory x linear function has a constant average rate of change he average rate of change between 4 2050 and 8 4100 is 512 5 ype an integer or a decimal he average rate of change between 8 4100 and 16 8200 is 512 5 Type an integer or a decimal

Find the derivatives of the function f for n 1 2 3 and 4 f x x sin x n 1 n 2 n 3 n 4 f x f x f x f x Use the results to write a general rule for f x in terms of n f x

K What conjecture can you make Make a conjecture Choose th A The sum is equal to th B The sum is the produc

4 9 16 25

Find f x and f c Function f x x 6x 9x 4x 7 f x f c Value of c C 0

Find the derivative of the function f for n 1 2 3 and 4 cos x xn n 1 n 2 n 3 n 4 f x f x f x f x f x Use the results to write a general rule for f x in terms of n f x

Product Quotient and Trig a Use the Product Rule to find the derivative of the given function b Find the derivative by multiplying the expressions first y 3 x 7 x Question 5 1 6 7 Part 1 of 3 a Use the Product Rule to find the derivative of the function Select the correct answer below and fill in the answer box es to complete your choice OA The derivative is x x OB The derivative is 3 x 7 x OC The derivative is 3 x 7 OD The derivative is 3 x 7 x 4

Let f x be a differentiable function such that f 5 2 and f 5 3 If g x x f x then find g 5 Give the exact value NO DECIMALS g 5

Use slopes to determine if the triangle whose vertices are 3 3 2 4 and 4 0 is a right triangle Find the slope for the side of the triangle between the vertices 3 3 and 2 4 Type an integer or a simplified fraction m

X Let f t 2t 14 and consider the two area functions A x f t dt and F x f t dt Complete parts a c x f t ff t 7 10 yaratan a woo younnolly wanapiga all The value of A 8 is 1 Simplify your answer The value of A 9 is 4 Simplify your answer Use geometry to find an expression for A x when x 27 x 14x 49 Type an expression using x as the variable b Evaluate F 11 and F 12 Then use geometry to find an expression for F x for all x2 10 The value of F 11 is 7 Simplify your answer The value of F 12 is 16 Simplify your answer Use geometry to find an expression for F x when x2 10 14x 40 Type an expression using x as the variable c Show that A x F x is a constant and that A x F x f x First prove A x F x is a constant Given A x x 14x 49 and F x x 14x 40 subtract F x from A x

Suppose that the functions fand g are defined as follows 3 x 7 f x X g x x 5 g Find Then give its domain using an interval or union of intervals f Simplify your answers

Find the real solutions of the equation 13 2t 6 15 Select the correct choice below and fill in any answer boxes within your choice OA The solution set is Simplify your answer Use a comma to separate answers as needed

Find the real solutions of the equa x 4x 21 X

Find the real solutions of the equ 1 2t 1 8

Find the real solutions of the e 3x 12

atch each graph to its function Reciprocal function Cube root function Cube function Constant function Absolute value function Square root function Identity function rag the function to the appropriate area below

Graph the function Identify three points on the graph f x x Given the x coordinates determine the y coordinates of three points on the graph X 1 0 1 Simplify your answers Type integers or decimals y

Find f a f a h and the difference quotient f x 4x 8 f a f a h f a h f a h f a h f a where h 0 h

1 Find all real Solutions of the equation E 1 8 X 2 x 4 7

A lottery game requires that 6 different numbers are picked from 1 to 12 If someone picks all 6 winning numbers the person wins 12 million Complete parts a and b below a How many ways are there to choose 6 numbers if order is not important There are ways to choose the numbers Type a whole number 27

cepts Solve Part 4 of 7 A pair of dice is rolled Find the probability of rolling a a sum not more than 3 b a sum not less than 11 c a sum between 4 and 9 exclusive 13 points Points 0 14 of 1 36 Simplify your answer Save How many ways can two dice be rolled such t that their sum is not more than 3 Simplity your answer The probability of roling a sum not more than 3 is 12 Type an integer or a simplified fraction b How many ways can two dice be rolled such that their sum is not less than 117

Assume that z and y represent positive real numbers Using the distributive property to help simplify the expression 2 36zy 9zy 3 100zy into the simplest radical form AVC where A and Care either integers or monomials Answer A and C

6 Use the graph of the function to answer the following questions 5 1 1 3 3 1 1 0 16 0 2 b What is the domain off 5 0 54 7 0 d List the interval s on which is decreasing e List the interval s on which f is increasing a For what values of x is f x 0 c What is the range of f

x 2 x 2 4 2 x Which of the following is equivalent to the express

Evaluate the derivative of this function In exp l o In k Ik

tg Graph of y f t The blue line in the f y plane shown above has the equation y f t This defines the linear function f a Consider the function A z f f t dt 0 Find an algebraic expression for A z valid for any z 2 A z for z 2 b Find F t the antiderivative for the function f t that obeys F 0 0 F t c Functions are identical if they give the same output values for every input The name of the variable used to define the function is irrelevant in testi condition True or False select The functions A and F are identical on the interval 5 00 True

Find a vector in the direction of 2 5 with length 2 Just state your answer in a b form

Find the exact value of the indicated trigonometric function of 0 8 cos 8 7 tan 0 0 Find sin 0 Find the reference angle for the given angle 9 381 Use reference angles to find the exact value of the expression Do not use a calcula

Given the points P 3 3 2 and Q 1 4 1 find PQ and QP Express your answers in the form a b c

Use the discriminant to determine the number of real solutions of the equation Do not solve the equation 4x 2x 11 0 4 O infinitely many real solutions two distinct real solutions one real solution O no real solution

Evaluate the indefinit integral sin 9x dx

At Anna s birthday party children who attended the party were given party gifts which were in the shape of an inverted cone The radius of the cone is x cm and the height is x 10 cm circumference of the cones was decorated by a velvet ribbon The capacity of the cone The cones were filled with candy and the y is two more than 33 times its circumference Which system of equations can be used to represent this situation OA y 3 10x y 33x 2 OB y 3 101 y 66mx 10 OC y 3 10x y 2 1 OD y x 10x y 66mg 2

A car drives down a road in such a way that its velocity in m s at time t seconds is v t 2t 2 Find the car s average velocity in m s between t 4 and t 8 4

Find the interval on which the curve 1 y 5 t 2 de dt is concave upward Note When using interval notation in WeBWork you use I for I for and U for the union symbol Interval

c Find the number of combinations of 2 elements take b B 22 2 21 2 2 121 Find the number of combinations of 2 elements taken 2 a C 2C 1

The graph below is comprised of transformation of tool kit functions 6 f x 7 3 q O 7 4 3 2 1 Me N my 2 las Complete a piecewise defined function that describes the graph if x 1 st if x 1 10 10

2 a b Find dx y coth lnx y x tanh Vx

Use the graph of y f x to answer the following V T O 3 2 34 2 1 2 3 4 y f x 2 3 x

4 3 Part 1 of 8 to Part 2 of 8 a Determine f 2 f 2 2 F 2 3 4 X y f x S

Question 24 8 3 36 O Points 0 of 1 Iro wants to adopt a puppy from an animal shelter At the shelter he finds eight puppie nale puppy from each of the four breeds of beagle boxer collie and Labrador The pu ejandro cannot make up his mind so he decides to pick the dog randomly e probability that Alejandro chooses anything except a female collie or a female boxer bability is n integer or a simplified fraction

Encuentra las coordenadas de la intersecci n de las diagonales del paralelogramo con los v rtices Q 1 3 R 5 2 S 1 2 y T 5 1 Las coordenadas de la inf

Find the derivative of the function y sin 6x 1

5 x if x 1 if x 1 a By considering limits prove that f is continuous at x 1 The function R R is defined by f x x b Show using first principles that f is not differentiable at x 1

Differentiate the function y xox y

Differentiate the function y x cos x y

Solve each equation for x a e2 4x X 9 b In 3x 18 2 X

Differentiate the function y etan 8 y

Distance in yards How long is a pass from the 5 yard line 20 yards from the sideline to the 45 yard line 50 yards from the same sideline