Question 1 Given f, f', and f" below (a) (b) 10(1-x) 10(1+2z) f(x)=(5-2x), f'(x) = f(x) 3x1/3 9x4/3 X x²+9 f(x) f'(x) f" (z) x² 9' (x² - 9)2' 2r(x²+27) (x-9)3 Sketch the curve of f by.... ⚫finding its domain. ⚫ finding the x- and y-intercepts, if any. ⚫ finding the equations of the horizontal and vertical asymptotes, if any. ⚫finding the interval of monotonicity. ⚫finding the intervals of concavity. ⚫ finding the inflection points, if any. Label any intercepts, asymptotes, and inflection points. Question 2 Consider the functions and their derivatives from Question 1, both (a) and (b). (a) Use the first derivative test to find the local extrema (if any). (b) Use the second derivative test to find the local extrema (if any). (c) Only for f(x) = (5 - 2x) x ³. Does one test seem to perform better than the other? Feel free to use your work from Question 1. Question 3 axb Find constants a and b in the function f(x): local minimum at x = In(x) such that f(): =1 and the function has a 2

Question 1 Given f, f', and f" below (a) (b) 10(1-x) 10(1+2z) f(x)=(5-2x), f'(x) = f(x) 3x1/3 9x4/3 X x²+9 f(x) f'(x) f" (z) x² 9' (x² - 9)2' 2r(x²+27) (x-9)3 Sketch the curve of f by.... ⚫finding its domain. ⚫ finding the x- and y-intercepts, if any. ⚫ finding the equations of the horizontal and vertical asymptotes, if any. ⚫finding the interval of monotonicity. ⚫finding the intervals of concavity. ⚫ finding the inflection points, if any. Label any intercepts, asymptotes, and inflection points. Question 2 Consider the functions and their derivatives from Question 1, both (a) and (b). (a) Use the first derivative test to find the local extrema (if any). (b) Use the second derivative test to find the local extrema (if any). (c) Only for f(x) = (5 - 2x) x ³. Does one test seem to perform better than the other? Feel free to use your work from Question 1. Question 3 axb Find constants a and b in the function f(x): local minimum at x = In(x) such that f(): =1 and the function has a 2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Solve this question please
Solve Question 1 , 2 and 3
Please help me solve question 14 Thank you
Please solve question 5.
Solve Question 4
Calculus I May I please have the solution to the following question? Thank you