Question

While studying MVT in single variable calculus the professor mentioned a consequence of mvt that is that if f' is 0 then the function is constant but i think its not so because if you look at a parabolic fuction that is symmetric about y axis and you take the values of a=-u and b=+u then the parallel would be the tangent at the minimum at which f' would have been zero

Answer 1

this is what i mean