Concept explainers
The graph of f′ is shown in the figure. Sketch the graph of f if f is continuous on [0, 3] and f(0) = −1.
To sketch: The graph of the function
Explanation of Solution
Given data:
Refer to the Figure in the textbook for the given function
The function
Formula used:
The antiderivative function for the function
Here, C is the constant.
Calculation:
The function
From the given figure in the textbook, the function
Rewrite the function
Use the antiderivative formula and find the antiderivative function
Rewrite the function as follows.
As
Rewrite the expression as follows.
Substitute –1 for
Substitute –1 for C in equation (3),
From equation (4), the at
Rewrite the function in equation (2) as follows.
From equation (5), as
Rewrite the expression as follows.
Substitute 1 for
Substitute 0 for D in equation (6),
From equation (7), the at
Rewrite the function in equation (2) as follows.
From equation (8), as
Rewrite the expression as follows.
Substitute 2 for
Substitute 4 for E in equation (9),
As the function is continuous on
Sketch the graph of the function
Thus, the graph of the function
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Precalculus (6th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus
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