Use the graph of f and g. P(x) = f(x)g(x) %3D f(x) 9(x) = g(x) %3D 107

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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Use the graph of f and g.
P(x) = f(x)g(x)
f(x)
q(x) =
g(x)
%3D
10
8-
4-
2.
4.
10
-2
(a) Find p'(5).
p'(5) =
(b) Find q'(8).
q'(8) =
2 Type here to search
Transcribed Image Text:Use the graph of f and g. P(x) = f(x)g(x) f(x) q(x) = g(x) %3D 10 8- 4- 2. 4. 10 -2 (a) Find p'(5). p'(5) = (b) Find q'(8). q'(8) = 2 Type here to search
Expert Solution
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.

p\left(x\right)=f\left(x\right)g\left(x\right)

take derivative

p'\left(x\right)=\frac{d}{dx}\left(f\left(x\right)g\left(x\right)\right)

p'\left(x\right)=f\left(x\right)\cdot g'\left(x\right)+g\left(x\right)\cdot f'\left(x\right)

take x=5

p'\left(5\right)=f\left(5\right)\cdot g'\left(5\right)+g\left(5\right)\cdot f'\left(5\right)

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