Question

Determine the average rate of change of the function f(t)=6+cos(t) over the interval [0, pi/4].

Answer 1

please help

Answer 2

the average rate of change of \(f\) over \([a,b]\) is just:$$\frac{f(b)-f(a)}{b-a}$$

Answer 3

I was trying to use that formula but I got nowhere..

Answer 4

hence we have$$\frac{f(\pi/4)-f(0)}{\pi/4-0}=\frac{(6+\cos(\pi/4))-(6+\cos(0))}{\pi/4}=\frac4\pi(\cos(\pi/4)-1)=\frac4\pi\left(\frac{\sqrt2}2-1\right)$$

Answer 5

I couldn't see the last bit but I got the correct answer with:

(4((1/sqrt(2))-1))/pi

thanks

Answer 6

right, it was just \(-1)\) that got cut off -- that's correct