what is the average rate of change for the function f(x)=4x^2 - 3 on the interval - 2≤x≤1?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 1$, and $f(x)=4x^{2}-3$.

Step2: Calculate $f(-2)$

Substitute $x=-2$ into $f(x)$: $f(-2)=4\times(-2)^{2}-3=4\times4 - 3=16 - 3=13$.

Step3: Calculate $f(1)$

Substitute $x = 1$ into $f(x)$: $f(1)=4\times1^{2}-3=4 - 3=1$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(b)-f(a)}{b - a}$, we have $\frac{f(1)-f(-2)}{1-(-2)}=\frac{1 - 13}{1+2}=\frac{-12}{3}=-4$.

Answer:

$-4$