Chapter 2, Problem 1SYU

To determine

To indicate:

Whether the statement is true or false.

Answer to Problem 1SYU

The statement “The derivative of f at $a$ is the instantaneous rate of change of f at the point $a$ ” is true.

Explanation of Solution

Given information:

The given statement “The derivative of f at $a$ is the instantaneous rate of change of f at the point $a$ ”.

We know that the derivative of function at any point is the rate of change of function at that point.

The mathematical expression for that can be written as follows,

$f\text{'}\left(a\right)=\frac{f\left(a+h\right)-f\left(a\right)}{a+h-a}$ Here $h$ is small positive value.

Hence the statement “The derivative of f at $a$ is the instantaneous rate of change of f at the point $a$ ” is true.