Let $f$ be a function that has domain: the closed interval $-1,6$ and range: the closed interval $-10,2.$ Let $f(-1)=2,f(0)=0,$ and $f(6)=-2.$ Let $f$ have the derivative $f^{\text{'}}$ that is continuous and have the graph shown in the figure above.

a$.$ Find all values of $x$ for which $f$ assumes a relative minimum. Give a reason for your answer.

b$.$ Find all values of $x$ for which $f$ assumes its absolute maximum. Justify your answer.

c$.$ Find the intervals on which $f$ is concave upward.

d$.$ Find all values of $x$ for which $f$ has a point of inflection. Give a reason for your answer.

e$.$ On the axes provided, sketch the graph of f$.$