Let f be any function continuous on [a, b] and twice differentiable on (a, b). If for all x ∈( a, b ), f^′(x)>0 and f^′ ′(x)<0, then for any c ∈( a,…

Let $\displaystyle f$ be any function continuous on [a, b] and twice differentiable on (a, b). If for all $\displaystyle x \in(\mathrm{a}, \mathrm{b}), f^{\prime}(x)>0$ and $\displaystyle f^{\prime \prime}(x)<0$, then for any $\displaystyle \mathrm{c} \in(\mathrm{a}, \mathrm{b}), \frac{f(\mathrm{c})-f(\mathrm{a})}{f(\mathrm{~b})-f(\mathrm{c})}$ is greater than: