Find the limit as x approaches c of the average rate of change of the function from c to x.
-c = 9; $$f ( x ) = \frac { x } { 3 } + 10$$
A) 3
B) Does not exist
C) 13
D) $$\frac { 1 } { 3 }$$

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 $f(x) = \frac{x}{3} + 10$, substituting $c = 9$ gives $\frac{\left(\frac{x}{3} + 10\right) - \left(\frac{9}{3} + 10\right)}{x - 9}$. Simplifying this expression leads to $\frac{\frac{x}{3} - 3}{x - 9}$, which further simplifies to $\frac{1}{3}$ as the constant terms cancel out and the variable terms simplify. Therefore, the limit as $x$ approaches $c$ (or 9 in this case) of the average rate of change of the function is $\frac{1}{3}$.

Find the Limit as X Approaches C of the Average f(x)=x3+10f ( x ) = \frac { x } { 3 } + 10f(x)=3x​+10

Find the Limit as X Approaches C of the Average $f ( x ) = \frac { x } { 3 } + 10$