Find the limit as x approaches c of the average rate of change of the function from c to x.
-c = 3; $$f ( x ) = 3 x ^ { 2 } + 39 x$$
A) 108
B) 57
C) 30
D) 90

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 the given function $f(x) = 3x^2 + 39x$ and $c = 3$, we first find $f(c) = 3(3)^2 + 39(3) = 27 + 117 = 144$. Then, the average rate of change from $c$ to $x$ is $\frac{3x^2 + 39x - 144}{x - 3}$. Factoring the numerator gives $\frac{3(x^2 + 13x - 48)}{x - 3}$ = $\frac{3(x - 3)(x + 16)}{x - 3}$, which simplifies to $3(x + 16)$ when $x \neq 3$. Taking the limit as $x$ approaches $3$, we get $3(3 + 16) = 3(19) = 57$.

Find the Limit as X Approaches C of the Average f(x)=3x2+39xf ( x ) = 3 x ^ { 2 } + 39 xf(x)=3x2+39x

Find the Limit as X Approaches C of the Average $f ( x ) = 3 x ^ { 2 } + 39 x$