Hi, please I need help with this demonstration:
If “f” , “g” :[ 0,1]→R are continuous functions, they are differentiable in (0,1), f(0)=0, g(0)=2 and │f ‘ (x)│≤1 ,│g ‘ (x)│≤1 for the interval (0,1). Prove that f(x) < g(x) in [0,1).
if g' is-1 which is as negative as it could be then g will be +1 at x=1 which is as low as it could be anywhere in the interval.
Meanwhile f' could be+1 which would also make f = +1 at x = 1 which is a big as it could be.
therefore f is always less than 1 and g always above 1 in the interval