If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x).
(a) Find u'(l).
(b) Find v'(5).
(a)
To find: The derivative of
Answer to Problem 45E
The derivative of
Explanation of Solution
Given:
The function is
Derivative rule:
Product Rule:
Calculation:
Obtain the value of
Apply the product rule (1) and simplify the terms,
Substitute 1 for x in
From the given graph, it is observed that
Obtain the values
Since the slope of the line at every point is equal, the slope of the function
Therefore, the value of
The slope of the function
Therefore, the value of
Substitute the values
Therefore, the derivative of
(b)
To find: The derivative of
Answer to Problem 45E
The derivative of
Explanation of Solution
Given:
The function is
Derivative rule:
Quotient Rule: If
Calculation:
Obtain the value of
Apply the Quotient rule (1) and simplify the terms,
Substitute 5 for x in
From the given graph, it is observed that
Obtain the values
Since the slope of the line at every point is equal, the slope of the function
Therefore, the value of
The slope of the function
Therefore, the value of
Substitute the values
Therefore, the derivative of
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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Precalculus Enhanced with Graphing Utilities (7th Edition)
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