Application of derivatives Questions and Answers

As on the previous page f x 4x 7x 2 c Find the equation of the line tangent to f x at x 1 d Find the equation of the line normal to f x at x 1 e At which values of a is the tangent line horizontal

6 10 Functions and Their Graphs Use the equation y x 16 to answer parts a through g below ordered pair B There are no x intercepts Ques f Sketch the graph Ure the graphing tool to graph the equation y x 16

average rate of change of the function between x 1 and x 1 b Find f x using the limit definition of the derivative f x h f x

7 Table 2 1 p 20 summarized frequency of seatbelt use while driving for twelfth grade participants in the 2003 Youth Risk Behavior Surveillance System YRBSS survey In 2001 YRBSS survey students were asked the same question For the 2001 survey a summary of responses given by 2530 students in the twelfth grade who said that they drive follows Wears Seatbelt Never Rarely Sometimes Frequency 105 248 286 464 1427 Most times Always Source http www cdc gov nccdphp dash yrbs a What percent of the twelfth grade students who drive said that they always wear a seatbelt when driving b What percent of the twelfth grade students who drive said that they do not always wear a seatbelt when they drive c Find the percentage in each of the five response categories d Draw a bar graph of the percentages found in part c

Convert the quantity to the indicat 13 pounds to kilograms 13 lb kg Round to the nea

Solve the system of equations by the subs y x 3 x y 4

Integrate fete dr dx O e x C O None of the above O e e x x C e x

ume Par A cardboard box is 56 cm long a Round all given numbers to b Compute the actual volume

Suppose that V t 14 1 07 3 sin t represents the value of a person s investment portfolio in thousands of dollars in year t where t 0 corresponds to January 1 2020 Round each answer below to two places after the decimal At what instantaneous rate is the portfolio s value changing on January 1 2022 thousands of dollars per year Determine the value of V 2 What do your answers above tell you about the way the portfolio s value is changing on January 1 2022 O the value of the portfolio is increasing but its rate of increase is slowing down O the value of the portfolio is increasing and its rate of increase is speeding up O the value of the portfolio is decreasing and its rate of decrease is speeding up O the value of the portfolio is decreasing but its rate of decrease is slowing down

19 2 Points DETAILS TANAPCALO Use the graph of the function f to determine the f x x x

Question 2 If f x 2 sin x 12 cos x then f 4 Question Help Video

work 2 2 Sine and C 0 10 answered tion 10

ework 2 2 Sine and 7 15 0 10 answered estion 5 the equation of the tangent

Let A 0 2 4 6 8 10 B 0 1 2 3 4 5 6 and C 4 5 6 7 8 9 10 Find AUB nC 0 2 3

3 Find the derivative of the function 6 f t 7 3t 5 a b C d r e 18 7 31 3 f t 7 31 5 7 f t 7 31 18 f t 1 31 7 f t 3 7 3t

Determine which of the following sets are equivalent BNC BUC 1 U U B 2 AU BU 3 An BUC Only 1 and 2 are equivalent Only 1 and 3 are equivalent 1 2 and 3 are all equivalent Only 2 and 3 are equivalent None of the sets are equivalent

Let U n Z n 4 be the universal set Consider the subsets A 2 0 1 2 3 and B ne Unis even Determine each of the following cardinalities AU B An Bl A P 1 A

Use the labeled Venn diagram to find AB C A 1 00 23 4 5 9 4 7 25 Select all regions which would be included 7 6 3 B 8

1 point Suppose that F x f t dt where Find F 2 2 f t nt4 S 7 u4 U du

1 Grapns Draw the graph of the function and state the domain and range f x 4x 1 OA The domain of this function is Type your answer in interval notation Use integ any numbers in the expression Th domain is all real numbers

Question 2 1 Clear my choice Which of the following

10 points Determine a recurrence relation for the coefficients in the power series about xo 0 for the general solution of 1 x y y y xe Use this to write the first five nonzero terms i e all terms up to order 4 inclusive of the general solution

6 Use the Quotient Rule to differentiate the function 9x x 7 f x

lim tan 2x X 0

What are the features of the function f x log x 1 graphed below 12 11 10 9 8 7 3 12 11 10 9 8 7 6 5 4 3 2 1 M 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 The function f x is function with a asymptote of The range of the function is and it is x on its domain of behavior on the LEFT side is as The end the RIGHT side is as and the end behavior on 3

Consider the function fx A x 4x 5 5074 find any holes if they exist

er the parameter is eliminated the equation becomes x y ace

in the blank ystem of equations that has no solution is called system of equations that has no solution is calle

1 Graphs Draw the graph of the function and state the d 1

Draw the graph of the function and state 3 y 15

Let f x 10x 8 17e Then the equation of the tangent line to the graph of f x at the point 0 9 is given by y mx b for m b

2 For the quadratic function f x x 6x answer parts a through c a Graph the quadratic function by determining whether its graph opens up or down and by finding its vertex axis of symmetry y intercept and x intercepts if any Does the graph of f open up or down up down What are the coordinates of the vertex The vertex of the parabola is 3 9 Type an ordered pair Use integers or fractions for any numbers in the expression What is the equation of the axis of symmetry The axis of symmetry is x 3 Type an equation What is are the x intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice A The x intercept s is are Type an integer or a decimal Use a comma to separate answers as needed B There are no x intercepts

Let f x 11 ln x 11 Then f x is and f 9 is f x is and f 9 is 11 9 WE MOOSE ww

Entered x 3 y 3 4 At least one of the answers above is NOT correct Answer Preview 1 4 Follow the steps to find the equation of the tangent line to the curve 2 4 512 at the point 4 4 This problem has two parts You may only open the next part after correctly completing the previous part Implicit Differentiation Tangent Line The formula for the tangent line is y 4 Result correct correct incorrect

Find d dx 6 Type In x for the natural logarithm function Pho RON 10 AMAR pa Mo 2 100

Find the equation of the tangent line to the graph of 6 sin 2x at the indicated x value f x 6 sin 2x x 0 help formulas The formula for the tangent line is y

nvertible function f a is given along with a point that lies on its graph Using Theorem 2 7 7 evaluate f z at the indicated value f a 0e Point 0 6 100 help numbers

The function fis defined as follows f x 3 int x a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range e Is f continuous on its domain a The domain of the function fis 00 Type your answer in interval notation b Locate any intercepts Select the correct choice below and if necessary fill in the answer box to complete your of A The intercept is 1 0 OB The intercepts are x 0 for 0 x 1 OC There are no intercepts

Find bounds on the real 3 f x x x x 2x 2

se the area model to divide 20x 3 3x 2 17x 7 4x 2 x 3

What is the advantage of ABC over Job Order Costing Multiple Choice O ABC is less costly to implement than Job Order Costing Using multiple cost drivers makes overhead allocation more accurate Job Order Costing is not allowed by U S GAAP

Derivat lc I Chapter 3 Part II ly in the direction of your dreams Thoreau K ON EACH PROBLEM FOR ANY PARTIAL CR 257 The formula for the volume of a sphere is S e Suppose a spherical snowball is melting in the s t are decreasing 1 ose r 13 1 2 where t is time in minutes t 1 ich the snowball is melting

Determine whether the graph is a function If it does repr give its domain and range OB The domain is all real numbers OC The domain cannot be determined because the function What is the range Select the correct choice below and if necessary fill in complete your choice

8214 O 8142 Question 4 0 5 points Listen Use Newton s method to det 1 1 x correct to fo I

Compute the directional derivative of the following function at the given point P in the direction of the given vector Be sure to use a unit vector for the direction vector f x y 9 x 3y P 3 3 Find the gradient of f x y Vf x y 1 3 10 10 9 x 3y

Is this set of ordered pairs a fu Yes No

Shiing Shen Chern s credit card company determines his minimum monthly payment by adding all new interest to 1 of the outstanding principal The credit card company charges an interest rate of 0 038726 per day On March 17 Shiing uses his credit card to purchase airline tickets for his family for 3500 He makes no other purchases during March Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer parts a and b below KIIB a Assuming Shiing had no new interest determine Shiing s minimum payment due on April 1 his billing date Shiing s minimum payment due on April 1 is 35 b On April 1 instead of making the minimum payment Shiing makes a payment of 400 Assuming there are no additional charges or cash advances determine Shiing s minimum payment due on May 1 Shiing s minimum payment due on May 1 is

a A x has domain 4 3 range 2 5 and DOES have an inverse function y b B x has domain 1 00 range 0 00 and DOES NOT have an inverse function y

A cubic polynomial function f has a leading coefficient of 2 and a constant term of 5 When f 2 5 and f 2 13 what is f 1 5

Let lim 5 f x 10 and lim 5 g x 1 Find lim 5