5-Consider the quadratic function f (x) = ax2 + bx + c defined on the interval [2, 4]. The Mean Value Theorem guarantees that there must be a number between 2 and 4 (call it z) such that the tangent line at (z, f (z)) has the same slope as the line connecting (2, f (2)) and (4, f (4)). (8 pts.) a) Find z. b) Which one of the following statements does characterize z? (circle the right answer.) 1) z is independent of the values of a, b, and c. 2) z varies depending on what a, b, or c are. c) What would the value of z be if the same function was defined on the interval [1, 4]? (Just give the value. No need to show your work.) d) Make a conjecture (an educated guess) about the location of z in any given interval