Does there exist a function f such that f(0)=-1, f(2)= 4, and f'(x) is less than or equal to 2 for all x

Question

hartnn · Answer

so could you find the slope between those 2 points ? 0,-1 and 2,4 ?? i see you are also referring to http://openstudy.com/study#/updates/5278061be4b0275c53860afe

hartnn · Answer

@angel2015

anonymous · Answer

Yes I did and I got 5/2

hartnn · Answer

sorry for the late reply
yes, f'(x)  can be 5/2 = 2.5
but we are given f'(x) $\le2$
so is it possible that such a function f exist ?

hartnn · Answer

since 2.5 > 2 
and f'(x) less than or = 2 for all x,
such function f cannot exist :)