Question

Supose that 0 < f'(x) < 1/2 for all x-values. Show that f(-1) < f(1) < [2 + f(-1)]

Answer 1

inequality in integral:
int0]-1 to 1 <intf']-1 to 1 <int 1/2 ]-1 to 1

0<f(1)-f(-1)<1/2(1--1)-> f(-1)<f(1)<2+f(-1)

Answer 2

hmmm - I think I can show this visually as follows: