Concept explainers
To explain: The difference between the absolute maximum and the
Explanation of Solution
Absolute maximum:
A function f has an absolute maximum at
Local maximum:
A function f has
Local maximum does not attain at extreme values.
Difference between the absolute maximum and the local maximum:
From the above definitions, the local maximum is any one of the maximum value available in the curve whereas the absolute maximum is the highest maximum of the curve. That is, the highest point of the curve is called as absolute maximum.
Therefore, it can be concluded that any absolute maximum is called as local maximum but not the vice versa.
Consider an example as shown below in Figure 1.
From Figure 1, it is observed that,
Thus, the absolute maximum of
Also, it can be observed that,
Thus, the local maximum of
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Chapter 4 Solutions
Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th (James Stewart Calculus)
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