*f*(*x*) is continuous on [0,2] and differentiable on (0,2). The Mean Value Theorem says there is some *c* in (0,2) for which *f*'(c) is equal to the slope of the secant line between (0,*f*(0) and (2,*f*(*2*)), which is
$$\frac{*f*(*2*)-*f*(0)}{2-0} = \frac{4-0}2 = 2.$$ Here's the picture: | |