Question

For all twice differentiable functions f : R → R, with f(0) = f(1) = f'(0) = 0 

(1) f"(x) = 0, for some x ∈ (0, 1) 

(2) f"(0) = 0 

(3) f"(x) ≠ 0 at every point x ∈ (0, 1) 

(4) f"(x) = 0 at every point x ∈ (0, 1)

Answer 1

(1) f"(x) = 0, for some x ∈ (0, 1)