Answer
$27$
Work Step by Step
The general formula for average rate of change from $a$ to $b$ can be written as: $\dfrac{f(b)-f(a)}{b-a}$
Here, we have: $f(x)=x^3-27=(x-3)(x^2+3x+9)$
Thus, we find the average rate of change as:
$\lim\limits_{x\to 3}\dfrac{f(x)-f(3)}{x-3}=\lim\limits_{x\to 3}\dfrac{(x^3-27)}{x-3} \\=\lim\limits_{x\to 3}\dfrac{(x-3)(x^2+3x+9)}{x-3} \\=\lim\limits_{x\to 3} (x^2+3x+9)\\=[3^2+3(3)+9] \\=27$
