Chapter 10.1, Problem 57E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Revenue** The weekly revenue of a certain recently released film is given by

*R* is in millions of dollars and *t* is in weeks.

(a) Find the critical values.

(b) For how many weeks will weekly revenue increase?

**(a)**

To determine

**To calculate:** The critical values of the function *R* is in millions of dollars and *t* is in weeks.

Explanation

**Given Information:**

The provided equation is

**Formula Used:**

As per the First Derivative Test,

Step 1: Evaluate the first derivative of the function is evaluated.

Step 2: The first derivative is made equal to zero in order to get the critical points that satisfy

**Calculation:**

Consider the provided equation,

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

Hence, there will no change in the values of critical values as in the derivative graph.

Take out the first derivative of the equation by the power rule,

**(b)**

To determine

**To calculate:** The weeks for that weekly revenue will increase. Where, the function *R* is in millions of dollars and *t* is in weeks.

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