TRUE OR FALSE: Assume that g is differentiable on an open interval (a, b). Then a point c ∈ (a, b) is an extrema point of g if and only if g′(c) = 0.

Question

TRUE OR FALSE: Assume that g is differentiable on an open interval (a, b). Then a point c ∈ (a, b) is an extrema point of g if and only if g′(c) = 0.

Answer 1

NO

the first derivative gives the critical points where the tangent line has slope zero.

the SECOND derivative tells whether it is max or min