Question

Suppose $f$ is a twice-differentiable function with $f(0) = 0$, $f\left(\frac12\right) = \frac12$ and $f'(0) = 0$. Prove that $f''(x) \ge 4$ for some $x \in \left[0,\frac12\right]$.

Answer 1

Suppose f is a twice-differentiable function with f(0)=0, f(12)=12 and f′(0)=0. Prove that |f″(x)|≥4 for some x∈[0,12]. Could someone help ...