Chapter 1.2, Problem 4E

Find ${\max }_{a\le x\le b}|f(x)|$ for the following functions and intervals.

1. $f(x)=\left(2-e^x+2x\right)/3,[0,1]$
2. $f(x)=(4x-3)/\left(x^2-2x\right),[0.5,1]$
3. $f(x)=2x\cos (2x)-{(x-2)}^2,[2,4]$
4. $f(x)=1+e^{-\cos (x-1)},[1,2]$