Given the following values, find h ′(1) for each of the functions below. f(1) = 1f'(1)=2ƒ'(3) = −5(a) Chain Rule: h(x) = f(g(x))(b) Product Rule: h(x) = f(x) · g(x)(c) Quotient Rule: h(x)=f(x)g(x)=h'(1) ==⇒ h'(1) =h'(1) =-20=2910g(1) = 3gʻ(1) = 4g'(3) = 0

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f(1) = 1 ƒ'(1) = 2 ƒ'(3) = -5 (a) Chain Rule: h(x) = f(g(x)) ⇒ (b) Product Rule: h(x) = f(x) · g(x) f(x) g(x) (c) Quotient Rule: h(x): = h'(1) = -20 h'(1) = h'(1) = 2 9 10 g(1) = 3 g'(1) = 4 g'(3) = 0

f(1) = 1 ƒ'(1) = 2 ƒ'(3) = -5 (a) Chain Rule: h(x) = f(g(x)) ⇒ (b) Product Rule: h(x) = f(x) · g(x) f(x) g(x) (c) Quotient Rule: h(x): = h'(1) = -20 h'(1) = h'(1) = 2 9 10 g(1) = 3 g'(1) = 4 g'(3) = 0

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

Given the following values, find h ′(1) for each of the functions below.

f(1) = 1
f'(1)=2
ƒ'(3) = −5
(a) Chain Rule: h(x) = f(g(x))
(b) Product Rule: h(x) = f(x) · g(x)
(c) Quotient Rule: h(x)
=
f(x)
g(x)
=
h'(1) =
=
⇒ h'(1) =
h'(1) =
-20
=
29
10
g(1) = 3
gʻ(1) = 4
g'(3) = 0

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