Letf, g be functions. Suppose we know thatƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3.Using the above information, compute h' (-6) where h(x) = (f(x))² g(x).h'(- 6) = Number

The given function and derivative values,.The aim is to find the value of where .

Answered: Letf, g be functions. Suppose we know…

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...

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Question

Letf, g be functions. Suppose we know that
ƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3.
Using the above information, compute h' (-6) where h(x) = (f(x))² g(x).
h'(- 6) = Number

Expert Solution

Step 1: Given the information

The given function and derivative values,

$f open parentheses negative 6 close parentheses equals 4 comma space f apostrophe open parentheses negative 6 close parentheses equals negative 4 comma space g open parentheses negative 6 close parentheses equals negative 4 comma space g apostrophe open parentheses negative 6 close parentheses equals negative 3$ .

The aim is to find the value of $h apostrophe open parentheses negative 6 close parentheses$ where $h open parentheses x close parentheses equals open parentheses f open parentheses x close parentheses close parentheses squared g open parentheses x close parentheses$ .