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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

CONCEPT CHECK

First Derivative Test Describe the First Derivative Test in your own words.

To determine

The First derivative test.

Explanation

Given:

A function f(x).

The first derivative test is used to determine the relative extremes of a function with the help of the first order differential.

A number in the domain is said to be the critical point of a function if the value of the first derivative at that point is zero.

So, for a critical point c of a function f(x), the following applies:

If the derivative of the function, f(x) changes sign from a negative value to a positive value at the point c, then f is said to have a relative minima at the point c.

If the derivative of the function, f(x) changes sign from a positive value to a negative value at the point c, then f is said to have a relative maxima at the point c.

If the derivative function does not change sign at the critical point, the point is neither a maxima nor a minima.

Example:

Consider the following function:

g(x)=2x2x

Differentiate both sides with respect to x and equate the differential to zero to obtain the critical points,

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