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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Explain the difference between an absolute minimum and a local minimum.

To determine

To explain: The difference between the absolute minimum and the local minimum.

Explanation

Definition used:

Absolute minimum:

A function f has an absolute minimum at c if f(c)f(x)x in the domain (D) of f. The number c is called the maximum value of f on D.

Local minimum:

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

Local minimum and local maximum does not attain at extreme values.

Difference between the absolute minimum and the local minimum:

From the above definitions, the local minimum is any one of the minimum value available in the curve whereas the absolute minimum is the highest minimum of the curve. That is, the least point of the curve is called as absolute minimum

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