Question

given the function $f(x) = x^2 - 3x - 5$, determine the average rate of change of the function over the interval $-2 \leq x \leq 3$.

Explanation:

Step1: Define average rate formula

The average rate of change of $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$

Step2: Calculate $f(-2)$

$f(-2)=(-2)^2-3(-2)-5=4+6-5=5$

Step3: Calculate $f(3)$

$f(3)=(3)^2-3(3)-5=9-9-5=-5$

Step4: Compute average rate

$\frac{f(3)-f(-2)}{3-(-2)}=\frac{-5-5}{3+2}=\frac{-10}{5}=-2$

Answer:

$-2$