In order for the mean value theorem to be applicable, f(x) needs to be continuous on the entire closed interval [0;2], and differentiable in its interior ]0;2[.

Continuity at x=0 requires a=3, and you can determine the requisite values of b and m from the tangent to the graph of at . Because, for f(x) to be differentiable at the graph must be that tangent itself...