Consider the function

$$ f(\mathrm{x})=\frac{x^3}{3}+\frac{7}{2} x^2+10 x+\frac{133}{2}, x \in[-8,0] . $$

Which of the following statements is/are correct?

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a twice-differentiable function and suppose its second derivative

satisfies $f^{\prime \prime}(x)>0$ for all $x \in \mathbb{R}$. Which of the following statements is/are ALWAYS correct?

Let $\quad f: \mathbb{R} \rightarrow \mathbb{R} \quad$ be such that $|f(x)-f(y)| \leq(x-y)^2$ for all $x, y \in \mathbb{R}$.

Then $\quad f(1)-f(0)=$ ____________