(Solved): 5. A function f is continuous and twice differentiable for all values of x. The figure above shows ...

5. A function $f$ is continuous and twice differentiable for all values of $x$. The figure above shows the graph of $f^{?}$, the derivative of function $f$ on the closed interval $[?4,2]$. The graph of $f^{?}$ has horizontal tangents at $x=?1$ and $x=1.5$. The areas of regions $A,B$, and $C$ are 20,10 , and 6 , respectively, and $f(2)=3$. (A) Find all $x$-values on $(?4,2)$ such that the function $f$ has a local minimum. Justify your answer. (B) Find all $x$-values on $(?4,2)$ such that the graph of $f$ has a point of inflection. Justify your answer. (C) Evaluate ${\lim }_{x?1}\frac{2f(x)}{x+1}$. Explain your reasoning. (D) Evaluate ${\lim }_{x??2}\frac{f(x)+1}{x+2}$. Explain your reasoning.