Answer the following question and show all working.

4. A function reaches its relative maximum if the function is concave at its critical point (i.e., A point in the domain of a function where the first derivative is equal to zero). A function reaches its relative minimum if the function is convex at its critical point. (8 points) Given these definitions, from the following TC function, TC = Q3 - 502 + 60Q Find, a. The Average Cost Function (AC) b. The Critical Value (i.e., value of Q where the first derivative is equal to zero) c. Whether the function AC is minimized/maximized at this critical point? d. The minimum average cost