Differentiation Questions and Answers

The temperature change T in Fahrenheit degrees in a patient that is generated by a dose q in milliliters of a drug is given by the function T f q What does it mean to say f 45 1 5 If a patient takes a dose of 45mL of a drug the patient will experience a body temperature change of 1 5 degrees F If a patient takes a does of 1 5 mL of a drug the patient will experience a body temperature change of 45 degrees F Part 1 of 2 Olf a patient takes a degrees of a drug the patient will experience a body temperature change of T ml A person s sensitivity s to the drug is defined by the function s q f q What are the units of sensitivity degrees Fahrenheit per milliliter Part 2 of 2 Suppose that f 45 0 02 Write a complete the following sentence to explain the meaning of this value The sentence will include information given in the first question For a patient taking a expect a temperature change that is about ml dose adding 1 more ml to the dose leads us to degrees less than

The velocity of a ball that has been tossed vertically in the air is given by v t 48 32t where v is measured in feet per second ft s and t is measured in seconds The ball is in the air from t 0 until t 3 When is the ball s velocity greatest Determine the value of v 1 v 1

A laboratory study investigating the relationship between diet and weight in adult humans found that the weight of a subject W in pounds was a function W f c of the average number of Calories C consumed by the subject in a day In the statement f 1500 195 Hint What are the units of 1500 cal What are the units of 195 lb In the statement f 1900 0 Hint What are the units of 1900 cal What are the units of 0 lb cal In the statement f 225 2500 Hint What are the units of 225 lb What are the units of 2500 cal dW de What are the units of f c lb cal Suppose that Sam reads about f in this study and draws the following conclusion If Marissa increases her average calorie intake from 2800 to 2850 calories per day then her weight will increase by approximately 0 8 pounds Fill in the blanks below so that the equation supports her conclusion

A particle is moving along the curve f a As it passes throught the point 5 3 its instantaneous rate of change is 6 We also know that if you draw the tangent line to this curve at the point 4 8 it will be a horizontal ta this information find the value of f 5 f 4 f 5 012 018 017 013 09

A garden is in the shape of a rectangle 43 feet long and 20 feet wide If fencing costs 6 a foot what will it cost to place fencing around the garden OA 378 OB 756 OC 5 160 OD 1 512

For each of the following series tell whether or not you can apply the Alternating Series Test If you can apply this test enter D if the series diverges or C if the series converges If you can t apply this test even if you know how the series behaves by some other test enter N NOTE Make sure that you can provide the proper arguments to support your answers N 3 4 5 6 8888WWW n 1 n 1 n 1 n 1 n 1 1 cos nn n5 1 en n 1 n n 1 n nn 1 n en 1 n 5 Activ Go to

Differentiate y Im x 3 x 5 x 4 lm x 3 x 5 x 4 0

Differentiate the function y In 5x 4x 1 y 0

ab ab ab Question 2 as Write your question below What is the domain for the function f x x 1 Interval

VE bo x Solve the equation 13x 11 10 Show yo Round to one decimal place as needed Solution 1 Solu

22 X 3 12 2

27 What is the value of n if 8 2n 3 28 What is the value of a if 272 9a 29 If 3a 1 x and 3a 30 If 25b 1 x and 5b y express y in terms of x x and 5b y express x in terms of

If h 2 9 and h 2 3 find d h x dx X 13 6 X x 2 Ws Enhanced Feedback Please try again You have to use the Quotient Rule to solve this problem To apply the Qu d f x x a x f x

b Find the derivative by expanding the product first h z 5 2 2 22 5 a Use the product rule to find the derivative of the given function Select the correct answer below and fill in the answer box es to complete your choice OA The derivative is 2 2z 5 OB The derivative is 5 2 2 2z 5 OC The derivative is 5 2 2 2z 5 OD The derivative is 5 z 2 2z 5 OE The derivative is 5 2

The temperature T of a person during an illness is given by T t a Find the rate of change of the temperature with respect to time b Find the temperature at t 1 hr c Find the rate of change of the temperature at t 1 hr 98 6 where T is the temperature in degrees Fahre 1 2 a Find the rate of change of the temperature with respect to time 5 1 2 2 T t b Find the temperature at t 1 hr T 1 F Round to two decimal places as needed

In t years the population of a certain city grows from 100 000 to a size P given by P t 100 000 400C dP a Find the growth rate dt b Find the population after 15 yr c Find the growth rate at t 15 d Explain the meaning of the answer to part c B

Find an equation of the tangent line to the graph of y The tangent to the curve at the origin is y 0 2x 2 1 at the origin and at the point 1 1 www

6200 R v V can be used to determine the heart rate R of a person whose heart pumps 6200 milliliters mL of blood per minute and v milliliters of blood per beat Complete parts a through c below a Find the rate of change of heart rate with respect to v the output per beat R v b Find the heart rate at v 50 mL per beat The heart rate is beats min Round to two decimal places as needed c Find the rate of change at v 50 mL per beat The rate of change is beats min per mL Round to two decimal places as needed Heart rate 200 R v 100 100 Output per beat 200

5 Use the graph and the function to find the following a Find lim k x x 4 b Find k 4 c Is k continuous at x 4 a Select the correct choice below and fill in any answer boxes in your choice OA lim k x x 4 Round to the nearest integer as needed OB The limit does not exist b Select the correct choice below and fill in any answer boxes in your choice OA K 4 Round to the nearest integer as needed OB The function is undefined at x 4 c Is k continuous at x 4 O Yes O No CLB H AN Ay F but d 2 5 4 8 24 K

Find the derivative dx dx 3 X 3 X

Find the derivative of the following function y 9x y 3 2 2x 1 12 8

Question 8 Given f x 1 24 and g z 16 x 3 find the domain of f g x

Divide 10x 19x 6x 14 9x 2x 1 Write your answer in the following form Quotient 10x 19x 6x 14 9x 2x 1 0 Remainder 2x 1 0 2x 1

A Cepheid variable star is a star whose brightness alternately increases and decreases Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 4 7 days Its average brightness is 4 4 and the brightness changes by 0 6 Using this data we can construct a mathematical model for the brightness of Cephel Joe at time t where t is measured in days B t 4 4 0 6 sin 2xt 4 7 a Find the rate of change of the brightness after t days Rate of change b Find the rate of increase after one day Rate of increase

Match the functions and their derivatives 1 y cos tan x 2 y sin z tan z 3 y tan z 4 y cos x A y 1 tan z B y sin x tan z sec z cos 1 C y sin tan x cos

c Sketch the graph of p x arctan x and then sketch the graph of p x List all values of x for which p x is not differentiable 11 loto to b a Explain What does this say about

Given that f x 2x evaluate the function at x 3 6 12 O 6 12 5 1 point If we are evaluating the function f x then we cannot have the following f x 0 when x 0 f x 0 when a 0 All of the other answers are possible f x 0 when x 0

2 The displacement in meters of a particle moving in a straight line is given by the equation of motion s t a t 1 t 2 t 3 V V V V m s m s m s m s where t is measured in seconds Find the velocity in m s of the particle at times t a t 1 t 2 and

A ball is thrown into the air with a velocity of 39 ft s Its height in feet after t seconds is given by s t 39t 16t2 Find the velocity in ft s of the ball at time t 1 second ft s

Pluto has a radius of 700 miles As the planet rotates on its axis a point on its equator travels at 267 558 miles per year a Find the angular speed of a point on its equator in radians per year b Find the number of rotations the planet makes per year Do not round any intermediate computations and round your answer to the nearest whole number a Angular speed radians per year b Number of rotations per year X

Using scientific notation convert the following 1 nL mL Write your answer in the form of 1x10 to show an exponent due to formatting in C

Which of the following are continuous functions Select all that apply O The temperature at a specific location as a function of time The temperature at a specific time as a function of the distance due west from New York City The altitude above sea level as a function of the distance due west from New York City The cost of a taxi ride as a function of the distance traveled The current in the circuit for the lights in a room as a function of time None of these

In the figure below AABC AXZY Find cos Z sin Z and tan Z Round your answers to the nearest hundredth 38 5 cos z sinZ 0 0 tan Z 18 42 5 BO X S X

In the figure below AXYZ AABC Find tan B sin B and cos B Round your answers to the nearest hundredth X 15 2 tan B sin B cos B 0 0 0 28 5 32 3 Y B X

Find the values of a and b that make f continuous everywhere a b f x x 4 X 2 ax bx 3 2x a b if x 2 if 2 x 3 if x 3

18 5 10 5 ch 10 Given the graph of f x above find the following and write your answer in interval notation a Domain of f x b Range of f x

d y 1 x Determine whether Linear or nonlinear dx4 and Show all steps

3x 6 points and inflection points The relative extreme points are Type an ordered pair Simplify your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed The inflection point is Type an ordered pair Simplify your answer Use integers or fractions for any numbers in the expression Choose the correct graph of y 2x 3x 6 OB possible O C O D Submit test

erentiate the function using one or more of the differentiation rules 1 3x 5 y ion 19 of 20

Need Help Submit Answer Read It DETAILS 16 12 8 0 11 Points The quantity of oxygen that can dissolve in water depends on the temperature of the water So thermal pollution influences the oxygen content of water The graph shows how oxygen solubility S varies as a function of s mg L 20 4 Watch It 0 SCALCET9 2 7 053 8 16 24 32 40 T C MY NOTES a What is the meaning of the derivative S T What are its units OS T is the rate at which temperature changes with respect to the oxygen solubility The units are C mg L OS T is the rate at which temperature changes with respect to time The units are C s OS T is the current level of oxygen solubility for a given temperature The units are mg L OS T is the rate at which oxygen solubility changes with respect to the water temperature The units are mg L C OS T is the rate at which oxygen solubility changes with respect to the time The units are mg L s ASK

Determine whether f 0 exists x sin 0 O f 0 does exist O f 0 does not exist Need Help Submit Answer Read It if x 0 if x 0

If f x 9x x find f 1 and use it to find an equation of the tangent line to the curve y 9x x at the point 1 8 Need Help Submit Answer 10 0 11 Points Find f a f a f t Read It Watch It DETAILS SCALCET9 2 XP 7 012 MI 8t 60 t 9

d 24 Show that sec x dx sec x tan x

x PERIO 22x 2 f x tan z 3 sin x 3 cos x

7 0 1 Points A graphing calculator is recommended a Find the vertical asymptotes of the function y xx DETAILS SCALCET9 2 2 042 10 x 2 7x 4x b Confirm your answer to part a by graphing the function A graphing calculator is recommended y 10 1 10 10 Enter your answers as a comma separated list If an answer does not exist enter DNE 10 y 10 5 5 10 5 X 10 10 5 y 10 5 10 5 10 X 10 5 y 10 10

Note You can click on the graph to obtain a larger version in a new browser window The graphs of the function f given in blue and g given in red are plotted above Suppose that u x f x g x and v x f x g x Find each of the following u 1

0 13 Points DETAILS Find the limit If the limit is infinite enter co or co as appropriate If the limit does not otherwise exist enter DNE lim 25x x x 5

Find the equation of the line that is tangent to the curve at the point T 6T y 6x cos x The equation of this tangent line can be written in the form y mx b where and b

If f t t 6t 6 4t 2 4t 3 find f t

2 0 N 2 4 1 1 N 2 6 10 3 162 8 a Identify the parent function of the graph depicted in the image 10 bowered by desmos