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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