3) Consider the function g(x) given by y = 9-3x². a) Is g one-to-one on R? Be able to explain briefly why or why not. b) Does the inverse function y = g-¹(x) exist in the neighborhood of the point xº = 2? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x = = c) Does the inverse function y = 9-¹(x) exist in the neighborhood of the point x* = 0? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x=x*. 4) Let z = [e] = e.) e²(-¹) and x = €²(x-4) x-3 =y-y²+4. Calculate dz/dy and evaluate it at y = 1. (Note that

3) Consider the function g(x) given by y = 9-3x². a) Is g one-to-one on R? Be able to explain briefly why or why not. b) Does the inverse function y = g-¹(x) exist in the neighborhood of the point xº = 2? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x = = c) Does the inverse function y = 9-¹(x) exist in the neighborhood of the point x* = 0? (Be able to explain briefly why or why not.) If the answer is Yes, compute [g-¹(x)]' at x=x*. 4) Let z = [e] = e.) e²(-¹) and x = €²(x-4) x-3 =y-y²+4. Calculate dz/dy and evaluate it at y = 1. (Note that

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...

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