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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

EXPLORING CONCEPTS

Think About It S represents weekly sales of a product. What can be said of S' and S" for each of the following statements?

(a) The rate of change of sales is increasing.

(b) The rate of change of sales is constant.

(c) Sales are steady.

(d) Sales are declining but at a slower rate.

(a)

To determine

The nature of S' and S'' for the variable S that represents the total sales in a week for a particular product with the rate of change of sales is increasing.

Explanation

Given:

The variable S represents the total sales in a week for a particular product and the rate of change of sales is increasing.

The rate of change of sales be represented by the derivative of S, S'.

Now a function is said to be increasing on an interval if its derivative gives a positive value over that interval

(b)

To determine

The nature of S' and S'' for the variable S that represents the total sales in a week for a particular product with the rate of change of sales is constant.

(c)

To determine

The nature of S' and S'' for the variable S that represents the total sales in a week for a particular product with the sales are steady.

(d)

To determine

The nature of S' and S'' for the variable S that represents the total sales in a week for a particular product with the sales decreasing at a slower rate.

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