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8th Edition

James Stewart

ISBN: 9781285741550

To determine

**To explain:** The difference between the absolute maximum and the local maximum.

Explanation

**Absolute maximum**:

A function *f* has an absolute maximum at
*D* of *f*. The number
*f* on *D*.

**Local maximum**:

A function *f* has local minimum at *c* if there is an open interval *I* containing *c* (any *x* near to *c*) such that
*I*.

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,
*R.*

Thus, the absolute maximum of

Also, it can be observed that,

Thus, the local maximum of

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