Question

How do I find the average rate of change of `f(x) = tan x` from 0 to `pi/4`?

Answer 1

The average rate of change is the slope,

`(f(x+h)-f(x))/h=(f(b)-(a))/(b-a),` where `a` is the lower bound and `b` is the upper bound.

`(f(pi/4)-f(0))/(pi/4-0)=(tan(pi/4)-tan(0))/(pi/4-0)=(1-0)/(pi/4)=1/(pi/4)=1.2732`