Concept explainers
Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it.
Example 1
FIGURE 1
FIGURE 2
To sketch: The graph of
Explanation of Solution
From the given graph, it is observed that the graph of f contains the horizontal tangent at one point. Let the point be A.
Note that, the value of the derivative will be zero at the point where the function has the horizontal tangent.
Thus, the graph of
From the given graph, f has a vertical tangent line at the left end point. This implies that, the derivative function
From the point A to left, the slope of the graph f is positive which implies that the derivative graph
From the point A to right, the slope of the graph f is negative which implies that the derivative graph
From the given graph, f has a vertical tangent line at the right end point. This implies that, the derivative function
Graph:
Use the above information and obtain the graph of
Thus,
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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