Find the limit as x approaches c of the average rate of change of the function from c to x.
-$$c = 9 ; \quad f ( x ) = \frac { x } { 3 } + 10$$
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 $\frac{f(x) - f(c)}{x - c}$. Substituting $f(x) = \frac{x}{3} + 10$ and $c = 9$, we get $\frac{\left(\frac{x}{3} + 10\right) - \left(\frac{9}{3} + 10\right)}{x - 9}$. Simplifying, we find the average rate of change is $\frac{1}{3}$, which does not depend on $x$, so the limit as $x$ approaches $c$ is also $\frac{1}{3}$.

Find the Limit as X Approaches C of the Average c=9;f(x)=x3+10c = 9 ; \quad f ( x ) = \frac { x } { 3 } + 10c=9;f(x)=3x​+10

Find the Limit as X Approaches C of the Average $c = 9 ; \quad f ( x ) = \frac { x } { 3 } + 10$