Find the two x-intercepts of the function f and show that f (x) = 0 at some point between the two x-intercepts. f(x) = x2 - 2x - 15 ( x, y ) = ( -3,0 ) (smaller x-value) ( x, y ) = ( 5,0 ) (larger x-value) Find a value of x such that f '(x) = 0. X = XDetermine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = -x2 + 5x, [0, 5] 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). O No, because f(a) # f(b). 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.) C = XDetermine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 9 sin x, [0, 2x] Yes, Rolle's Theorem can be applied. O No, because f is not continuous on the closed interval [a, b]. O No, because f is not differentiable in the open interval (a, b). No, because f(a) # f(b). 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.) C = XDetermine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 9 cos nix, [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). 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.) C = XConsider the graph of the function f(x) = x2 + 7 (see figure). (1: 6) i2, 3} (a) Find the equation of the secant line joining the points (1, 6) and (2, 3). X (b) Use the Mean Value Theorem to determine a point C in the interval (1, 2) such that the tangent line at c is parallel to the secant line. X (c) Find the equation of the tangent line through c. X