Application of derivatives Questions and Answers

Determine the extreme values of the function F x on the closed interval 1 5 if F x Show your work Selected Answer Docponso 3 x 3x S 2 3 t dt None Given It looks like you did not solv

Find the derivative of the function f x In 3x 2 4x 5 F xv

Find the derivative of the function dx y 5e x 4 11

Graph of f x is shown Determine all critical numbers the nature of each critical number i e local maximum local minimum or neither and intervals of increase decrease of f x Explain how you found your answer 4 2 4 3 2 1 0 1 2 3 4 5 6 y f x 2 3 4 5 5

Find the derivative of the function s t In t ds dt

Find the X intercept s of the following function Select all correct answers Select all that apply 3 0 0 3 0 3 0 0 3 0 3 0 1 0 f x 15x 23x 28

etermine the equation of the parabola whose graph is given below Write your answer in General Form 8 7 6 5 4 3 2 w JIP 4 5678

Cermine the equation of the parabola whose graph is given below Write your answer 7 6 5 4 5 321 71 7 3 4 5 6 7

Determine the domain and range of the following parabola f x 2 x 6 5 Write your answer in interval notation in the bc below Provide your answer below

Determine the y intercept of the parabola whose graph is given below 6 H 432551 5 4 3 1 7 6 5 4 3 2 1 4567WNH 2 4 5 6 7 te your answer in the form x y and use fractions if necessary B 1 2 3 4 5 6 7 H

ermine the X intere 1 6 5 7 6 4 3 2 1 1967 WI F 456

Determine the equation of the parabola graphed below Note be sure to consider the negative sign already present in the template equation when entering your answer Provide your answer below 4 3 2 2 OT 0 25 T 2 3 4

Determine the axis of symmetry of the parabola whose graph is given below 4321654 Give your answer in the form x h 6 5 4 2 1 7 6 5 4 3 2 11 LLLLLL 1234567 1234567

Determine the equation of the parabola whose graph is given below Write your answer in General Form clow a racin 6 1 2 3 4 5 6 7

Determine the vertex of the parabola whose graph is given below suver nnbookOE 654321 7 6 5 4 3 2 1 6 H 4 1 2 1234567 3 I 4 5 6 1 2 3 4 5 6 7 Ho Give your answer as an ordered pair h k For example if you found the vertex was at 1 2 you would enter 1 3

Determine the direction in which the graph of the following parabola opens f x 3 x 5 6 Select the correct answer below O Up Down Left Right

Use the interactive graph to determine the value of x when f x 0 33 X 11 10 9 8 7 6 5 4 3 2 m 0 51 134 12 y 11 10 9 8 7 6 5 3 21 2 3 4 5 6 7 8 2 3 O 5 6 7 8 T X L

Find the derivative of the function 6 s t 46 71 6 5

Choose the correct graph of the equation OA OB CLIE O C

Find a parametric equation for the line that passes through the point P 1 0 9 and is parallel to the vector Q 4 2 6 Find a parametric equation for the line Choose the correct answer below O A x 4 t y 2 t z 6 9t B x 1 4t y 2 t z 6 9t O c x 4 t y 2t z 9 6t D x 1 4t y 2t z 9 6t

A 1 Find properties of sine functions 2EK Find the period of the sinusoidal function J KIN Simplify any fractions 6 5 4 3 2 1 0 1 2 3 4 5 6 fx J1 2 H X

We have found the following table of values of f h for various values of h close to 0 h 0 5 0 1 f h 46 125000 0 0001 34 481000 0 01 32 240801 h 0 5 0 1 0 01 f h 32 002400 0 0001 21 875000 29 679000 0 001 32 024008 0 001 31 976008 31 760799 31 997600 We note that the values of f h appear to approach the same number for values of h that are close to 0 on the left and the right side of 0 The number that is approached from both sic good estimation for the value of the limit To conclude estimate the value of lim 2 h 4 16 correct to six decimal places h 0 h

point P 6 1 5 9 a If Q is the point x mpQ ii 5 99 mpQ iii 5 999 mpQ iv 5 9999 mpQ v 6 1 mpQ vi 6 01 MpQ vii 6 001 MpQ les on the viii 6 0001 Man 5 x 2 5 x find the slope of the secant line PQ correct to six decimal places for the following values of x

A graphing calculator is recommended The displacement in centimeters of a particle s moving back and forth along a straight line is given by the equation s 3 sin xt 4 cos xt where t is measured in seconds Round your answers to two decimal places a Find the average velocity during each time period i 1 2 ii 1 1 1 iii 1 1 01 iv 1 1 001 cm s cm s cm s cm s b Estimate the instantaneous velocity of the particle when t 1 cm s

Consider the following X 4 lim X 8 X 8 If x is chosen to be sufficiently close to 8 with x greater than 8 then f x Determine the infinite limit 8 88 0 and f x can be made Select arbitrarily large positive arbitrarily small positive arbitrarily large negative arbitrarily small negative

Let f x Sx 2 lim f x x 1 x 2 a Find the following limits If an answer does not exist enter DNE lim f x x 1 O Yes No b Does lim f x exist x 1 if x 1 if x 1

Find the length in cm of an arc of a circle with radius 45 cm if the arc subtends a central angle of 20 cm If you have had difficulty with this problem you should look at Appendix D of your text

a State the value of f 1 f 1 b Estimate the value of f 2 f 2 c For what values of x is f x 2 Enter your answers as a comma separated list X 0 d Estimate the values of x such that f x 0 Enter your answers as a comma separated lis X e State the domain and range of f Enter your answer using interval notation domain range

Find the center and radius of the circle with equation x2 y2 18x 12y 81 0 center radius x y

After you answer or skip a tutorial part the answer key for that part is displayed and you cannot change your answer To complete the tutorial enter the final answer 2 3 4 5 4

c co 2 Given that tang value and is in the fourth quadrant find the other function 8

A table of values for f g f and g is given f x g x 3 2 1 8 7 2 X 1 2 3 a If h x f g x find h 1 h 1 b If H x g f x find H 2 H 2 f x 4 5 7 g x 6 7 9

The formula for integrating True O False fudv u dv by parts is uv

Estimate the integral by representing it in terms of area In other words Hraw a picture of the area the integral represents and find the area using geometry 1 x dx

5 Evaluate the integral using the substitution u x 2 x x 2 dx 5 43

7 Evaluate the integral 2dx S xln 8x S

Evaluate the indefinite integral arcsin x 1 x dx

Match the equation with the surface it defines Also identify the surface by type paraboloid ellipsoid etc 10x z y Which graph below shows the surface OA OB BELISCHE O C X

mine the graph of the hyperboloid x y 2 36 Choose the correct graph of the equation OA OC X X Z WAN B D X X 1

2 x y z 49 Choose the correct graph of the equation OA OC X X N Y S OB OD X X N

Determine the graph of the cylinder x y 36 Choose the correct graph of the equation OA Z 12 OB X O C Z

Find the point at which the line meets the plane x 2 6t y 1 3t z 4t x y z 3 The point is x y z 0 0 Type integers or simplified fractions

Match the equation with the surface it defines Identify the surface by type paraboloid ellipsoid etc 6x 5z 341 Choose the correct graph of the equation below A OB 3 OC

The vector v ai bj is perpendicular to the line ax by c Use this fact to find an equation of the line through P perpendicular to v Then draw a sketch of the line including v as a vector starting at the origin P 1 8 v 4i j The equation of the line is 4x y 4 Type an equation Choose the correct graph of the line and vector below OA AY 5 0 57 OB 5 T 10 CORMINA HTT G OC N G D 40 M AY O K

Express the vector P P2 in the form v v i v j v3k if P is the point 8 5 8 and P2 is the point 3 3 9 P P i i it Simplify your answers Ok BICICCOB

Pam and Erin start at the same point and begin rollerblading in different directions Pam is rollerblading west at a speed of 2 miles per hour Erin is rollerblading north at a speed of 4 miles per hour After how many hours will they be exactly 14 miles apart Round your answer to two decimal places Provide your answer below

Each of two bike rental shops charges a set fee plus an hourly rate for each rental The cost of renting a bike from two shops s shown in the table Provid Hours Rented Shop A Cost Shop B Cost S 9 7 25 27 Mike wants to rent a bike for a certain number of hours and realizes that it would cost the same at both shops For how many hours does Mike want to rent a bike Do not include units in your answer low 1 5

Question Abdul Bea Cassie and Diego are landscapers Each charges a set fee plus an hourly rate for a landscaping job as shown Total Charge Select the correct answer below Abdul Hours Worked Which landscaper charges the greatest set fee Bea 1 3 Abdul Bea Cassie Diego 40 45 45 80 85 75 100

In 2008 Jen had a collection of 44 shells In 2011 her collection had 107 shells Enter a linear model which represents the number of shells s in Jen s collection t years after 2007 Provide your answer below

Find an equation for the family of linear functions such that f 6 5 a f x 5 m x 6 b f x m x 5 5 c f x 6 m x 5