Name: Calculus 1 Date: Quiz 3.2 1. Determine whether Rolle's Theorem can be applied to the function f (x) = (x -3)(x+2)2 on the closed interval [-2,3] . If Rolle's Theorem can be applied, find all numbers c in the open interval (-2,3) such that f'(c) = 0 5. Determine aste their Rolle In Theorem A) Rolle's Theorem applies; 27- 12 can be applied to f ( x ) = B) Rolle's Theorem does not apply on The chod interval [-12, 12 C) Rolle's Theorem applies; at Roll's Theorem can be applied, D) Rolle's Theorem applies; fund all numbers c in The open interval (- 12, 12) such that I( c) = Q. E) Rolle's Theorem applies; 2. Determine whether the Mean Value Theorem can be applied to the function f(x) =x on the closed interval [0,4]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0,4) such that f'(c) = J (4)-f(0) 4-0 A) MVT does not apply B ) MVT applies; 2 C) MVT applies; 4 V/3 3 D) MVT applies; 1 E) MVT applies; 3 3. Determine whether Rolle's Theorem can be applied to the function f (x) = x2 -12x + 20 on the closed interval [2, 10]. If Rolle's Theorem can be applied, find all values of c in the open interval (2, 10) such that f'(c) = 0. A) Rolle's Theorem applies; c = 6 B) Rolle's Theorem applies; c = -6 C) Rolle's Theorem applies; c = 4 D) Rolle's Theorem applies; c = 8 E) Rolle's Theorem does not apply 4. which of The following functions passes Through the sent ( 0, 8 ) and satisfies $ 12) = 40 Version 1 Page 1