Consider the graph of the function f(x) = x2 X - 56. (a) Find the equation of the secant line joining the points (-6, -14), and (B, D)' (b) Use the Mean Value Theorem to determine a point c in the interval (6, B} such that the tangent line at c is parallel to the secant line. (c) Find the equation of the tangent line through c. (d) Use a graphing utility to graph f, the secant line, and the tangent line. 20- y 20- -40 -20 20 40 40 -20 20 X X -20 -60 O 60 OFind the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two x-intercepts. f(x) = x- - 5x - 14 ( x, y ) = ( -2,0 ) (smaller x-value) ( x , y ) = ( 0, - 14 ) (larger x-value) Find a value of x such that f '(x) = 0. X =Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = -x4+ 2x, [0, 2] Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) # f(b). X If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)Describe Rolle's Theorem. Let f be continuous on [a, b] and differentiable on (a, b). Rolle's Theorem says that if --Select--- v then there ---Select--- number c in (a, b) such that ---Select-- v