Application of derivatives Questions and Answers

Algebraically find the inverse function of f x 3 5e x Graph f f and the line y x on the same screen and check whether the graphs of f and f are reflections about the

Find the solution of the logarithmic equation 7 ln 2 x 0 in terms of exponentials or correct to four decimal places 8

Use the Laws of logarithms to rewrite the expression in a form with no logarithm of a product quotient or power After rewriting we have with the constant A 0 and the constant In ry In xy Aln x Bln y

Evaluate the following expressions a ln ell b eln6 c e In 3 d In 1 e

Que following exponential equation Express irrational solutions 49

suppose that the total cost function in dollars for the production of X units of a product is given by the equation shown below T C x 5760 60 x 0 1 x 2 Then the average cost of producing X items is represented by the following equation A C x frac text total cost x frac 5760 x 60 0 1 x a Find the Instantaneous rate of change of average cost with respect to the number of units produced at any level of productlon A C prime x b Find the level of production at which this rate of change equals zero X c At the value found in part b find the instantaneous rate of change of cost and find the average cost Instantaneous rate of change of cost average cost what do you notice The Instantaneous rate of change of cost equals the average cost The instantaneous rate of change of cost is greater than the average cost The Instantaneous rate of change of cost is less than the average cost

For each of the following examples sketch the bifurcation diagram dx dt x 2 ax 4 Show all the working that helped you get there including a phase portrait

Use synthetic division and the Remainder f x 4x 3 11x 2 3x 3 f 1 f 1

Rewrite the expression as an algebraic expresion in 2 tan sin x Note by algebraic we mean that the answer is not allowed to use trig functions or inverse trig functions It is allowed to in polynomials quotients and roots

Use a Venn diagram If n A 11 n B 1 n AV B

stion 27 of 32 1 point Question A 22 23 ction below to answer the following 1

1 point Given that f 7 5 and f 7 9 find an equation for the tangent line to the graph of y f x at x 7

24 2 c 4 The solution set is 0 a Part 2 of 4 b 6 0 C 0 c 4 The solution set is 0 0 0 0 0 0 8 0 0 0 0 X 8 QUO S 0 0 0 0 0 0

Determine if the relation defines y as a one to one function of x The relation does not define y as a one to one function of x The relation defines y as a one to one function of x X

ve the following system of equations for x and y Assume 0 1 and r 0 0 577 1 0 1 40 y 1 r 1 r x y 15 10x

1 Find the exponential function that models the data in the table below X V y 3 98 2 94 9 2 1 0 9 What is the exponential regression of the data 1 18 2 36 3 72 4 144

K The function f 1 f x 3 The inverse fu Simplify your

A produce buyer for a juice company is buying apples He ma extra large Write out the sample space and assume each out

a Graph f x 2X 16 b Find the zero of f x c Based on the graph solve f x 0 a Choose the correct graph of f x 2 16 below OA 20 Ay HHO B 20 Ay b At what point is f x equal to zero x 4 Simplify your answer c For what values of x is f x 0 O C Type your answer in interval notation 120 Ay HO OD 20 S

Solve the following logarithmic equation log 4x 3 Select the correct choice below and if necessary fill in the answer box complete your choice OA The solution set is Simplify your answer Type an exact answer Use a comma to separate answers as needed B There is no solution

producing the 10 001st smartphone is rtphones or falling at a production level of 10 000 smartphones ns that the average cost is Select Thus there is a differen at a production level of 10 000 smartp

Otitis media or middle ear infection is initially treated with effectiveness A is inexpensive safe and effective B is als the tree diagram to the right where the costs are estimated following a Find the expected cost of using each antibiotic to treat a

L x Use L x to approximate the numbers 0 9 and 0 99 Round your answers to four decimal places 0 9 0 99 Illustrate by graphing f and the tangent line y 2 2 y 3 5 10 15 4 2 1 y 2 1 1 2 3 4 5 X

For each function determine the long run behavior x 1 x 2 2 x 1 2 x 2 x 1 x 2 has Select an answer has Select an answer has Select an answer

For each function determine the long run behavior x 1 x 2 x 1 x 2 x 1 x 2 has Select an answer has Select an answer has Select an answer

Determine the equation of the line tangent to the following function at x f x x 2 5 x 4 y

In the last 10 years the population of Indonesia has grown at a rate of 1 12 per year to 258 316 051 If this rate continues what will be the population in 10 more years Round your answer to the nearest whole number

Let F be the function defined by F a Lit 2 2t dt Find an expression

Use the sum and difference identities to find the exact value You may have need of the quotient reciprocal or even odd identities as well sec F 13T 12

Consider the function P x 7x 3 4x 12 x 10 x There are at most x intercept s and at most turning points

Reverse the order of integration in the following integral 6 12 2x SS f x y dy dx 00 Reverse the order of integration 00 SS f x y dx dy 2 R

Evaluate the following integral as it is written 35 SS sy dy dix 8y 0 x 35 ff8y dy dx ay By 0 x

Find the expected value for the random variable x having the pro

Divide begin fraction 8 x to the power of 5 end power y over 25 z to the power of 6 end power end fraction divided by begin fraction 20 x y to the power of 4 end power over 15 z cubed end fraction

stic model P t 93 2638 0 1715t represents the percentage of households that do not own 1 0 0303e luate and interpret P 0 Evaluate P 0 Question 10 6 8 23 Part 4 of 5 90 5 d to one decimal place as needed sentence below best describes P 0 P 0 is the year no households had a personal computer P 0 is the year all households had a personal computer P 0 is the percentage of households without a personal computer in 1987 P 0 is the percentage of households with a personal computer in 1987 Use a graphing utility to graph P P t Choose the correct graph below

Under certain water conditions the free chlorine hypochlorous acid HOCI in a swimming pool decomposes according to the law of uninhibited decay After shocking a pool the pool boy Geoff tested the water and found the amount of free chlorine to be 2 6 parts per million ppm Twenty four hours later Geoff tested the water again and found the amount of free chlorine to be 2 2 ppm What will be the reading after 3 days that is 72 hours When the chlorine level reaches 1 0 ppm Geoff must shock the pool again How long can Geoff go before he must shock the pool again After 3 days or 72 hours the amount of free chlorine in the pool will be Do not round until the final answer Then round to the nearest hundredth as needed ppm

My courses SC MATH1507 M N C Assignments Assignment 2

SC MATH1507 N Assignments Assignment 2 A jar contains 43 differ different colour

113 3198 The logistic model P n models the probability as 1 0 115e0 0912n a percent that in a room of n people no two people share the same birthday Complete parts a d a Use a graphing utility to graph P P n Choose the correct graph below OA AP 100 0 0 n 100 OB AP 100 0 0 100 C AP 100 0 0 OD n 100 AP 100 0 0 b In a room of n 16 people what is the probability that no two share the same birthday Round to the nearest integer as needed r 100

93 2638 0 1715t The logistic model P t represents the percentage of 1 0 0303e households that do not own a personal computer t years since 1987 Complete parts a d a Evaluate and interpret P 0 Evaluate P 0 P 0 Round to one decimal place as needed

Write the K expression for an aqueous solution of hydrofluoric acid Note that either the numerator or denominator may contain more than one chemical species Enter the complete numerator in th top box and the complete denominator in the bottom box Remember to write the hydronium ion out as H O and not as H

the system of equations using Cramer s F 6x 6y 6 12x 12y 17

value of the determinant 5 5 1 1 2 4 lue of the determinant is

he system of equations using Cramer s Ru x y 3 x y 1

If y 2z ln x find the following y 0

336 tickseer plants Communicate and Justify Suki says the area of the triangle is 12cm 2 Emilia says the area of the triangle is 10cm 2 Find the area of the triangle and explain any errors the girls might have made

The graph of f x x x 1 and its tangent line at 1 3 is shown Evaluate f 3 3 1 3 1 0 1 f 3 18 X 3

Let h x k 5x 10 x k k Z The constant term equals 170 Find k

Let f x 4x4 Inx Then f x 0 f e 0

Find all solutions to the equation cos sin 2 9 pts