Application of derivatives Questions and Answers

20 I Use Cramer s rule to determine the value for A in the following partial fraction decomposition You do not need to determine the others frac 2 x 3 x 2 left x 2 1 right frac A x frac B x 2 frac C x 2 1 frac D x x 2 1

nimum at x 1 f x 8x 5x has one local min use the derivative to answer the ques his function has a local maximum at

9 answered flection point for the f comma If there is not two decimal places

work 3 1 Using 16 0 12 answered stion 10

Mark the critical points on the following graph 18 12 5 4 3 2 1 6 6 12 18 24 30 36 Clear All Draw Dot 2 4 er

on 5 ue ion f x 2x 33x 168x 4 has atives to algebraically find the answer to t I maximum at x

1 Evaluate using the table X f x g x 3 2 11 9 8 3 1 7 0 0 5 1 1 2 3 1 0 3 3 1 8 a fog 1 c gof 2 e g g 1 b fog 2 d gof 3 f 3

X a show that f A B f A f B Rewrite f A B by substituting A B for x in the given function A B f A B a Which law of exponents can be used to rewrite the expression above as a product OA as O c a a as t O E a 1 Rewrite the expression f A B as a product to show that f A B f A f B f A B Since each factor in the product above can be written as f A and f B f A B f A f B OB a ast OD 18 1 OF ab a b

adratic Functions An athlete whose event is the shot put releases a shot released at an angle of 30 its height f x in feet can horizontal distance in feet from its point of release U answers using the graph

99 Determine the x 2t ln t y 2t ln t concavity of the curve

3 1 Quadratic Functions K An athlete whose event is the shot put the right is released at an angle of 30 where x is the shot s horizontal distand through c and verify your answers us

Quadratic Functions K Consider the function a b Determine w Find the mini

p 16 8 20 16 Make substitutions and see they re true

Watch help video Evaluate d 3x5 t2 2t dt

7 2 sin 20 3 sin 0 0 9 cos 20 3 sin 0 1 11 2 sin 0 cos 0 1 13 sin 0 1 cos 0

17 30 Solving Trigonometric Equations Involving a Multiple o an Angle An equation is given a Find all solutions of the equation b Find the solutions in the interval 0 2TT 17 2 cos 30 1 18 2 sin 201 20 2 sin 30 1 0 22 8999 22 sec 40 2 0 19 2 cos 20 1 0 19MAXE 21 3 tan 30 1 0 Tomein 0 23 cos 1 0 2 25 2 sin V3 0 3 0 24 tan 3 0 4 26 sec 0 2 0 2 cos

25 38 Solving Trigonometric Equations Find all solutions of the given equation 25 cos 0 1 0 27 V2 sin 0 1 0 29 5 sin 0 1 0 31 3 tan 0 1 0 33 2 cos 0 1 0 35 tan 0 4 0 37 sec 0 2 001102 26 sin 0 1 0 28 2 cos 0 1 0 30 4 cos 0 1 0 32 cot 0 1 0 34 4 sin 0 3 0 36 9 sin 0 1 0 38 csc 0 4 0

the given equation Toups or to anobuloa an or anonulor ori 39 tan 0 4 2 cos 0 1 0 40 tan 0 2 16 sin 0 1 0 41 4 cos 0 4 cos A 1 0

53 cos 0 sin 0 2 cos 0 0 54 tan sin 0 sin 0 0

17 24 Solving Basic Trigonometric Equations Solve the equation and list six specific solutions 17 cos 0 19 sin 0 V3 2 V2 2 18 cos 0 2 20 sin 0 21 cos 0 0 28 22 tan 0 2 5 23 tan 0 10o ano 24 sin 0 0 9 3 2

17 28 Half Angle Formulas Use an appropriate Half Angle Formula to find the exact value of the expression 17 sin 15 18 tan 15

3 10 Double Angle Formulas Find sin 2x cos 2x and tan 2x from the given information 5 3 sin x 3 x in Quadrant I 13

55 58 Evaluating Expressions Involving Trigonometric Functions Evaluate each expression under the given conditions 55 cos 0 cos 0 3 0 in Quadrant IV 59 tan 3 in Quadrant II o

47 50 Expressions Involving Inverse Trigonometric Functions Write the given expression in terms of x and y only 1 47 cos sin x tan y 48 tan sin x cos y

33 tan x TT 3 3 tan x 1 3 tan x

15 20 Values of Trigonometric Functions Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number and then find its exact value 20011 o 15 sin 18 cos 27 cos 18 sin 27

A function is defined by z x y xy Identify the independent and dependent variables The independent variable s is are and the dependent variable s is are 1 Use a comma to separate answers as needed

18 4 points A5 First and Second derivative test Sketch a graph such that f x 0 on 1 1 f x 0 on 3 1 and 1 3 local maximu at x 0 local minima at x 2

mportant but she isn t sure where to get started Right now Maria s main goals are to build an emergency Maria are 21 years old Maria just started her first job in construction She knows saving is fund since she doesn t have any savings and start saving for retirement Her take home pay averages 2500 per month although it varies based on her hours and opportunities for overtime Each month she pays approximately 270 towards her student loans 900 on rent 220 on healthcare 130 on transit and 500 on food She comes to you to ask for advice on her savings plan Write your suggestions to Maria Make sure you address the following questions 1 Ideally what percentage of her income should Maria aim to save overall What savings goals are included in that percentage 2 What barriers might Maria face when trying to save more 3 What strategies would you recommend Maria use to meet her savings goals 4 What account type would be best for Maria to save for her long term goals like retirement Why

Take a look at the tallest mountains in the world Mountain Mount Everest K2 Kanchenjunga Lhotse Height ft 2 9035 x 104 2 8251 x 104 2 8169 x 104 2 7940 x 104 1 If Kanchenjunga jumped on top of Mount Everest what is their combined height 2 What is the difference between K2 and Lhotse 3 What is the sum of the two tallest mountains in the world 4 Subtract Lhotse s height from Kanchenjunga s height

Prove the identity 2 tan x 1 tan x sin 2x

Prove the identity 1 sin 2x sin 2x sec x csc x

Given the function P x x 1 x 5 its leading coefficient is 1 its y intercept is 0 Enter the intercepts from smallest to largest its intercepts are 1 When y x Invalid notation When y Input or for the answer Input or for the answer x and 5

For s x 2x 8x 5 3 a Identify the horizontal asymptotes if any b If the graph of the function has a horizontal asymptote determine the poir Separate multiple equations of asymptotes with commas as necessary Select The graph has no horizontal asymptotes The graph has at least one horizontal asymptote Equation s of the horizontal asymptote s y 2 Crossover point s

The vertices of a rectangle are R 5 5 S 1 5 T 1 1 and U 5 1 After a translation R is the point 0 13 Find the coordinates of U OA 10 7 B 0 7 OC 10 9 D 0 9

x 5x 3 4x 5 For t x a Identify the horizontal asymptotes if any b If the graph of the function has any horizontal asymptote determine the point if any where the graph crosses the h Write numbers as integers or simplified fractions If there is more than one answer use the and button Select None if applicable O The graph has no horizontal asymptotes O The graph has at least one horizontal asymptote Equation s of the horizontal asymptote s Crossover point s Cand DO X 0 0 0 0 None S

y 4 y 10y 16 Part 1 of 2 Simplify y Part 2 of 2 4 10y 16 11 y 2 y 8 If there is more than one restriction use the and button O There are restrictions on the variable y O There are no restrictions on the variable y y z 0 X

To find the extremities of an ellipse Select one O a b c O d Find the square root of each term Make the X term and then the Y term equal to zero Find the factors of the constant Use the X and Y extremities for one point

10 The number of zeros of f x 3x 0 7x 8x is 1 provided that each zero is counted according to its multiplic

Determine graphically any local and absolute extrema f x x 3x 10 The absolute minimum is Type an integer or a decimal rounded to two decimal places as needed Type N if there is no absolute min

A polynomial f x and one or more of its zeros are given f x 7x 62x 167x 102 4 i is a zero Part 0 3 Part 1 of 3 a Find all the zeros Write the answer in exact form If there is more than one answer separate them with a comma Select None if applicable The zeros of f x Ola 0 0 10 0 x None S

nalysis The work shown bel x 3 x 2 2 by x 1 the error

af g x is a polynomial with real coefficients and zeros of 3 multiplicity 3 2 multiplicity 3 51 and 4 31 what is the minimum degree of g x The minimum degree of g x is

Part 1 of 2 Factor f x given that 2 is a zero f x x 2 4x 7 x 6 Part 1 2 Part 2 of 2 Solve f x 0 Express your answers in exact simplest form The solution set is GO

equivalent of one square met an integer or a decimal

Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational function 16x 8x 1 f x 4x 3 The equation of the vertical asymptote is x The equation of the slant asymptote is y

Chapter 3 Mastery Quiz K Windchill temperatures can be calculat per hour Use the formula to answer pa C 35 74 0 6215t 35 74254

Use the graph to determine the equation of the vertical asymptote 5 4 3 2 5 3 2 He 2 3 4 S 1 2 3 4 5

Find all real zeros of the fun Enter the real zeros separat

Northland down deep eno W WORK ONE