# The expression for the instantaneous velocity in terms of the graph of f. ### 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, Problem 10RCC
To determine

## To find: The expression for the instantaneous velocity in terms of the graph of f.

Expert Solution

The instantaneous velocity of the function of f(t) at t=a is limtaf(t)f(a)ta.

### Explanation of Solution

Graph: Calculation:

The instantaneous velocity of the function of f(t) is the derivative of the function f(t)

From the graph the slope of the straight line at t=a is f(t)f(a)ta.

Known fact the slope of the function at t=a is equal to the derivative of the function at t=a.

Therefore, The instantaneous velocity of the function of f(t) at t=a is

limtaf(t)f(a)ta.

Velocity is slope of tangent to the position curve.

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