MATH SOLVE

3 months ago

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

Accepted Solution

A:

Answer:Average rate of change (A(x)) of y=f(x) over an interval [a, b] is given by:[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]As per the statement:Given:[tex]y=f(x)=\cos (2x)[/tex] and interval [tex][0, \frac{\pi}{2}][/tex]At x = 0[tex]f(0) = \cos (2(0)) = \cos (0) = 1[/tex]At [tex]x = \frac{\pi}{2}[/tex][tex]f(\frac{\pi}{2}) = \cos (2(\frac{\pi}{2})) = \cos (\pi) =-1[/tex]Substitute the given values in [1] we have;[tex]A(x) = \frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-0}[/tex]⇒[tex]A(x) = \frac{-1-1}{\frac{\pi}{2}}[/tex]⇒[tex]A(x) = \frac{-2}{\frac{\pi}{2}}[/tex]⇒[tex]A(x) = \frac{-4}{\pi}[/tex]Therefore, the average rate of change of y=cos(2x) on the interval [0, pi/2] is, [tex]\frac{-4}{\pi}[/tex]