Question

find the average rate of change of the function f(x) = (2x - 1)^2 + 3 on -1, 2.

Explanation:

Step1: Expand the function

$f(x)=(2x - 1)^2+3=(4x^2-4x + 1)+3=4x^2-4x+4$

Step2: Calculate $f(-1)$

$f(-1)=4\times(-1)^2-4\times(-1)+4=4 + 4+4=12$

Step3: Calculate $f(2)$

$f(2)=4\times2^2-4\times2+4=16-8 + 4=12$

Step4: Use average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here $a=-1$, $b = 2$. So $\frac{f(2)-f(-1)}{2-(-1)}=\frac{12 - 12}{3}=0$

Answer:

$0$