Question

What is the average rate of change of y=cos(2x) on the interval 0 pi/2?

Answer 1

Jesus is the answer to this 

Answer 2

Answer:

Average rate of change (A(x)) of y=f(x) over an interval [a, b] is given by:

$A(x) = \frac{f(b)-f(a)}{b-a}$

As per the statement:

Given:

$y=f(x)=\cos (2x)$ and interval $[0, \frac{\pi}{2}]$

At x = 0

$f(0) = \cos (2(0)) = \cos (0) = 1$

At $x = \frac{\pi}{2}$

$f(\frac{\pi}{2}) = \cos (2(\frac{\pi}{2})) = \cos (\pi) =-1$

Substitute the given values in [1] we have;

$A(x) = \frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-0}$

⇒$A(x) = \frac{-1-1}{\frac{\pi}{2}}$

⇒$A(x) = \frac{-2}{\frac{\pi}{2}}$

⇒$A(x) = \frac{-4}{\pi}$

Therefore, the  average rate of change of y=cos(2x) on the interval [0, pi/2] is, $\frac{-4}{\pi}$