Let the function, f:[-7,0] → R be continuous on [-7,0] and differentiable on (-7,0). If f(-7)=-3 and f^′(x) ≤ 2, for all x ∈(-7,0), then for all such…

Let the function, $\displaystyle f:[-7,0] \rightarrow \mathbf{R}$ be continuous on $\displaystyle [-7,0]$ and differentiable on $\displaystyle (-7,0)$. If $\displaystyle f(-7)=-3$ and $\displaystyle f^{\prime}(x) \leq 2$, for all $\displaystyle x \in(-7,0)$, then for all such functions $\displaystyle f$, $\displaystyle f(-1)+f(0)$ lies in the interval :