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Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770
Textbook Problem

Applying the First Derivative Test In

Exercises 23-56, (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is increasing or decreasing, (c) apply the

First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.

f ( x ) = x log 4 x

(a)

To determine

To calculate: The critical points for the provided function f(x)=xlog4x.

Explanation

Given:

The function f(x)=xlog4x.

Formula used:

The function f said to have a critical point at c if:

f'(c)=0

Or the derivative does not exist at c.

Calculation:

The provided function can be rewritten as:

f(x)=xlnxln4

It can be seen that the provided function is differentiable on the interval (0,)

(b)

To determine

To calculate: The interval where the first provided function f(x)=xlog4x is increasing or decreasing.

(c)

To determine

To calculate: The relative extrema of the function f(x)=xlog4x using the first derivative test.

(d)

To determine

To graph: The function f(x)=xlog4x and find the relative extrema.

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