Find the limit as x approaches c of the average rate of change of the function from c to x.
-c = 3; f(x) = 5x + 3
A) -5
B) 3
C) 5
D) -3

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ from $c$ to $x$ is given by the formula $\frac{f(x) - f(c)}{x - c}$. For $f(x) = 5x + 3$, when $c = 3$, we have $\frac{(5x + 3) - (5(3) + 3)}{x - 3} = \frac{5x + 3 - 15 - 3}{x - 3} = \frac{5x - 15}{x - 3} = 5$. Therefore, the limit as $x$ approaches $c$ of the average rate of change is 5.

Find the Limit as X Approaches C of the Average