How do you find the average rate of change of $f(x)=cot x$ over the interval [pi/4, 3pi/4]?

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Answer 1 · 2017-11-29T12:42:38

The average rate of change of $f(x)$ is $-1.27(2dp)$

$f(x) =cotx$

The average rate of change of a function from $x=pi/4$ to

$x=(3pi)/4$ is $(f((3pi)/4)-f(pi/4))/((3pi)/4-pi/4)$

$f((3pi)/4) = cot ((3pi)/4)= -1 and f((pi)/4) = cot(pi/4)= 1$

$:. (f((3pi)/4)-f(pi/4))/((3pi)/4-pi/4) = (-1-1)/((3pi)/4-pi/4)$

$=-2/(pi/2) = -4/pi ~~ -1.27(2dp)$

The average rate of change of $f(x)$ is $-1.27(2dp)$ [Ans]

How do you find the average rate of change of f(x)=cot xf(x)=cot x over the interval [pi/4, 3pi/4]?