Application of derivatives Questions and Answers

1 2 se the point slope formu ossible

mapping F in the space defined by first projecting U onto the plane through the origin with the normal 1 2 5 and then further mapping this projected vector with the linear mapping taking the vector x y z to the vector 2x 3y 3x 4y z x y z

wata released by the Department of Education regarding the rate percentage of ninth grade students who don t graduate in a ertain year showed that out of 50 states 15 states had an increase in the dropout rate during the past 2 years 14 states had a dropout rate of at least 30 during the past 2 years 23 states had an increase in the dropout rate and or a dropout rate of at least 30 during the past 2 years a How many states had both a dropout rate of at least 30 and an increase in the dropout rate over the 2 year period states b How many states had a dropout rate that was less than 30 but that had increased over the 2 year period states

em Problem Lis on of the tangent lin

roblem Problem List 3 5x 1 find f 1 d an equation of the tangent

The cross sectional area of a tree 4 5 feet from the ground is called its basal area The table shows the basal areas in square inches of Tree A over time The image shows the growth rate and initial basal area of Tree B Year t 0 Basal area A 120 Treeld 1 2 3 4 132 145 2 159 7 175 7 Growth rate 6 Initial basal area 154 in a Write the function that represents the basal area of each tree after t years Round the growth rate to the nearest hundredth The function for Tree A is A

The lowest point of y x2 is 0 0 this point is called vertex Where is the vertex of function y x 1 O 0 1 O 1 0 O 0 1 none of these answers

solve this inequality 2x 4 x 1 give your answer in interval notation note 0 1 0 1 O 1 none of these answers

A line goes through point 1 3 and is parallel to y axis What is equation of this line x 1 O y 3 Oy 3x 1 none of these answers

2 Prove by mathematical induction that for n E Z 1 5 9 4n 3 2n n Maxims

4 B f 1 is A Positive B Zero OC Negative 5 4 A Zero OB Negative C Positive 8 2 B5 4 2 2 9 Use the graph of the function f x above to complete the following f 1 is 2 3 5

Given g 1 1 g 5 8 and 5 xg x dx g x dx 6 find the indicated integral

D Evaluate the limit if it exists If an answer does not exist enter DNE 1 1 1 5 lim x X 5 lim t o X 5 X Evaluate the limit if it exists If an answer does not exist enter DNE 7 7 t Find common denom 7 t 7 t t 7 t 7

3 For n E Z let Pn be the proposition that 6 1 is divisible by 5 Prove the proposition true for all positive integers

Given the equation y 6 sin The amplitude is The period is The horizontal shift is The midline is 7T x 49 4 8 units to the Select an answer

Graph the solution set of the inequality where x i

Graph the solution set of the inequality wh x 7 3

Find the area of triangle ABC see the figure with the given information Round to the nearest tenth B A a a OA 422 0 sq km B 417 8 sq km OC 437 1 sq km D 431 3 6 km Y b 48 3 b 89 kilometers c 12 7 kilometers C

The time for a chemical reaction 7 in minutes is a function of the amount of catalyst present a in milliliters so T f a a If 6 15 what are the units of 6 What are the units of 15 What does this statement tell us about the reaction The units of 6 are The units of 15 are 6 15 tells us b lf 6 3 what are the units of 6 What are the units of 3 What does this statement tell us The units of 6 are The units of 3 are Pis

Find the area of the triangle by using Heron s formula Round the answer to the nearest tenth All sides are measured in inches a 15 7 b 14 9 c 14 3 OA 99 6 sq in OB 105 6 sq in O C 102 6 sq in OD 96 6 sq in

VITO Question 3 6 6 57 Graph the equation using the x and y intercepts 2x y 8 Use the graphing tool to graph the equation Use the intercepts when drawing the line If on one intercept exists use it and another point to draw the line Click to

Determine the slope of the line throu 2 4 and 7 11 elect the correct choice below and i A The slope is Tyne an integer or a simplified

Determine the slope of the lin 3 2 and 6 7

Find f g f g fg and f g and their domains f x x g x 8x Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find Find the domain of 4 x Enter your answer using interval notation

Evaluate the integral 5 F x 5 f x dx where 5 x 25 f x if 5 x 0 if 0 x 5

QUESTION 18 Simplify 24 2 3 12 X

QUESTION 21 Simplify 9 35 4 142 2 3 6 4

QUESTION 5 Simplify 2 3 12 3 I

2 Graph without technology only use transformations and an input output chart if needed Make sure you have 5 accurate points on your graph f x 3 x 2 1 8 7 6 32

A What is the vertex B What is the line or axis of symmetry in equation form C What are the x intercepts and the y intercept D What is the Domain F Increasing interval H End Behavior as x y E What is the Range G Decreasing interval AND as x y 1 Graph the function Make sure you graph the vertex and 4 additional fou noir 6 5 1 7 2 3 4 5 6

Parameterize the curve y e x for x n Put your answer in the form of a vector valued on F t BT We a tax x ex Y E Ja TX

5 Which number q makes the matrix A A 6 makes A r b have infinitely many solutions Justify your answers 14 2 17 6 not invertible Which value of t in 03 9 103 2 3 4 1 02 giving z y and z of the solution in terms of a b and c 6 Use the inverse of Az a 0 8 to find the unique solution to A y

0 1 Points 1 DETAILS Evaluate the limit if it exists If an answer does not exist enter DNE x 49 x 24 lim X 24 Need Help X PREVIOUS ANSWERS Read It SCALCCC5 2 25

1 2 Use the given graph to estimate the value of each deriva tive Then sketch the graph of f 1 a 3 c 1 e 1 g 3 1 1 b f 2 d f 0 f 2 X

13 If an equation of the tangent line to the curve y f x at the point where a 2 is y 4x 5 find f 2 and f 2

At River Bank checking account customers earn 0 75 interest a month on their account balances pay no service fees for writing checks and pay a monthly 2 00 financial charge Calculate the income earned in one month on the checking account for a customer with an account balance of 1 000 OA 4 25 OB 5 50 C 6 75 D 7 25

K Write the converse inverse and contrapositive of If I am in Seattle then I am in the West

1 Suppose f is the inverse function of a differentiable function f and f 6 6 f 6 3 Find f 6 13 6

For each of the given functions f x find the derivative f a at the given point a first finding b f a f x 6x 7x 7 a 13 b 1 a f x x 13x 55 on the interval 6 5 0 a 19 b 1 125 a

Enter a T or an F in each answer space below to indicate whether the corresponding statement is tr or false You must get all of the answers correct to receive credit 1 ln x y ln x ln y 2 In a b b ln a 3 ln ab In a ln b 4 In x In y In x ln y

K 6x 5 19 impl Choose the correct OA If 6x 24 th OB If 6x 24 th OC If 6x 5 1 OD If 6x 5 1

The function y f x is shown below 7 ta q 2 3 NY a a N LA b T to Determine the number of invariant points after each of the transformation on y f x and record your answer in the form abcd Transformation y f x y f x 2 f y y f x Number of Invariant Points tx C F Record your answer in the numerical response section below d

Find the 56th derivative of the function f x cos x The answer is function cos x

3 y 2y sin x dx x 2xy y sin 2x dy 0 Final Answer f x y C xy xy 3x y sin 2x 2 Pls show neat and whole solution

5 Let f x 2 csc x X df dx d f 5 2 2 cot x csc x 10 3

ye y 2y dx xe y 6xy 2y dy 0 Final Answer x y e y 2y x y f C Pls show neat and whole solution

Find the equation of the tangent line to the curve y 2 tana at the point 7 2 equation of this tangent line can be written in the form y mx b where m is and whoro bic TH

Suppose that the position of a particle is given by s f t 2t 3t 9 a Find the velocity at time t v t m b Find the velocity at time t 3 seconds 8 m 8 c Find the acceleration at time t a t m 82 m 82 d Find the acceleration at time t 3 seconds

2 Write the Maclaurin series for a f x In 1 x n 4 b f x e 2x n 5

nd the length of the following two dimensional curve 1 2t 1 3 2 2 3 r t 3 for 0 st 18 no an exact answer using radicals as needed