# The meaning of f ′ ( 8 ) and its units. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.6, Problem 50E

(a)

To determine

## The meaning of f′(8) and its units.

Expert Solution

### Explanation of Solution

Given:

Consider the function f(p) is a quantity (in pounds) of coffee is sold by a coffee company at a price of p dollars per pounds. That is Q=f(p).

Note that, the derivative f(x) is the instantaneous rate of change of the function f(x) with respect to x

The derivative f(p) is the rate of change of quantity (in pounds) of coffee is sold with respect to price of p dollars per pounds.

The derivative f(8) is the rate of change of quantity (in pounds) of coffee is sold with respect to price of 8 dollars per pounds.

The instantaneous rate of change is equal to f(t)=limΔx0ΔyΔt    here y=f(t).

Here Δy is measured in pounds and Δt is measured in dollars.

Thus, the units are pounds per dollars.

(b)

To determine

Expert Solution

### Explanation of Solution

The derivative f(8) is the rate of change of quantity (in pounds) of coffee is sold with respect to price of 8 dollars per pounds.

Since the quantity of coffee is sold is decrease when the price is increasing.

If price is 8 dollars, then the quantity of coffee sold will decreasing.

Thus, the value f(8) is negative.

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