A twice-differentiable function is convex iff its second derivative is nonnegative everywhere

Let $𝑓 : (𝑎, 𝑏) \to ℝ$ be a $𝐶 2$ differentiable function. Then $𝑓$ is convex iff $𝑓 ″ (𝑥) \geq 0$ for all $𝑥 \in (𝑎, 𝑏)$ . anal Furthermore if $𝑓 ″ (𝑥) > 0$ for all $𝑥 \in (𝑎, 𝑏)$ , then $𝑓$ is strictly convex.