   Chapter 9.3, Problem 3CP ### 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

# Which of the following are given by f ' ( c ) ?(a) The slope of the tangent when x =   c (b) The y-coordinate of the point where x =   c (c) The instantaneous rate of change of f ( x )  at  x =   c (d) The marginal revenue at x   =   c  if  f ( x ) is the revenue function

To determine

The correct options given by f(c), from the provided choices.

Explanation

Given Information:

The provided choices are

(a) The slope of the tangent when x=c.

(b) The y-coordinate of the point where x=c.

(c) The instantaneous rate of change of f(x) at x=c.

(d) The marginal revenue at x=c if f(x) is the revenue function.

Explanation:

Derivative of a function has several interpretations, all of which are calculated by the same technique.

The interpretations are

To obtain the velocity, f(x) is an interpretation of derivative because velocity is the rate of change of distance that an object moves, over a period of time.

To obtain the instantaneous rate of change of a function, f(x) is an interpretation of derivative because the instantaneous rate is the rate of change of the function, instantly

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