Question

what is the average rate of change of y = cos(2x) on the interval 0, π/2?
a -4/π
b -1
c 0
d √2/2
e 4/π

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b=\frac{\pi}{2}$, and $f(x)=\cos(2x)$.

Step2: Calculate $f(0)$ and $f(\frac{\pi}{2})$

When $x = 0$, $f(0)=\cos(2\times0)=\cos(0)=1$. When $x=\frac{\pi}{2}$, $f(\frac{\pi}{2})=\cos(2\times\frac{\pi}{2})=\cos(\pi)=- 1$.

Step3: Compute the average rate of change

Substitute into the formula: $\frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-0}=\frac{-1 - 1}{\frac{\pi}{2}}=\frac{-2}{\frac{\pi}{2}}=-\frac{4}{\pi}$.

Answer:

A. $-\frac{4}{\pi}$