   Chapter 10.1, Problem 57E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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 ( t ) = 50 t t 2 + 36 ,   t ≥ 0 where 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(t)=50tt2+36,t0 if the weekly revenue of a certain recently releases film is given as above; where, R is in millions of dollars and t is in weeks.

Explanation

Given Information:

The provided equation is R(t)=50tt2+36,t0.

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 f(x)=0. The values which makes first derivative of the function undefined known as critical values.

Calculation:

Consider the provided equation,

R(t)=50tt2+36,t0

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,

R=(t2+36)(50)50t(2t)</

(b)

To determine

To calculate: The weeks for that weekly revenue will increase. Where, the function R(t)=50tt2+36,t0 is increasing if the weekly revenue of a certain recently releases film is given as above; where, R is in millions of dollars and t is in weeks.

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