Chapter 13, Problem 7RCC

a.

To determine

To find: the expression.

Answer to Problem 7RCC

the expression is $\frac{dy}{dx}=\frac{1}{2}$.

Explanation of Solution

Given information:

The average rate of change of $y$ with respect to $x$ between the numbers $a$ and $x$.

Calculation: to find the average rate of change, first write the function then differentiate,

  $y=\frac{a+x}{2}$

Now, differentiate the function,

  $\frac{dy}{dx}=\frac{1}{2}$

b.

To determine

To find: the expression.

Answer to Problem 7RCC

the expression is $y\text{'}=\underset{x\to a}{\lim }f\text{'}\left(x\right)$.

Explanation of Solution

Given information:

The instantaneous rate of change of $y$ with respect to $x$ at $x=a$.

Calculation: to find the average rate of change, first write the function then differentiate,

  $y=f\left(x\right)$

Now, differentiate the function,

  $y\text{'}=\underset{x\to a}{\lim }f\text{'}\left(x\right)$