   Chapter 10.1, Problem 49E ### 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

# Advertising and sales Suppose that the daily sales (in dollars) t days after the end of an advertising campaign are given by S = 1000 + 400 t + 1 , t ≥ 0 Does S increase for all t   ≥ 0 , decrease for all t   ≥ 0 , , or change direction at some point?

To determine

Whether the S increase for all t0, decrease for all t0, or change direction at some point if the daily sales which is in dollars, t days after the end of an advertising campaign are as S=1000+400t+1,t0.

Explanation

Given Information:

The provided function is S=1000+400t+1,t0.

Explanation:

Consider the provided function S=1000+400t+1,t0,

The first derivative is made equal to zero in order to get the critical points.

The values of the critical values are kept inside the original function which gives the critical points. The intervals of the values of x are then evaluated for the relative maximum and minimum.

For differentiable function f on an interval (a,b),

If f(x)>0 the function f is increasing for all x in the interval (a,b).

If f(x)<0 the function f is decreasing for all x in the interval (a,b).

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

ddt(S)=ddt(1000+400t+1)=ddt(1000)+ddt(400t+1)=0400(t+1)2S=400(t+1)2

Put the value of S=0,

S=400(t+1)2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 