Graphically and using derivatives, find the values guaranteed to exist by Rolle's theorem. Determine if the requirements for Rolle's theorem are met by the function f left parenthesis x right parenthesis equals short dash 2 x cubed plus 54 x plus 5 on the interval left square bracket short dash 3 comma space 6 right square bracket. If so, find the values of c in left parenthesis short dash 3 comma space 6 right parenthesis guaranteed by the theorem. A.) f left parenthesis x right parenthesis is a polynomial so it is continuous on left square bracket short dash 3 comma space 6 right square bracket and differentiable on left parenthesis short dash 3 comma space 6 right parenthesis. When evaluated, f left parenthesis short dash 3 right parenthesis equals short dash 103 and f left parenthesis 6 right parenthesis equals short dash 103. Therefore, f left parenthesis a right parenthesis equals f left parenthesis b right parenthesis and the conditions of Rolle's theorem are met. The value guaranteed by Rolle's theorem is c equals 3. B.) f left parenthesis x right parenthesis is a polynomial so it is continuous on left square bracket short dash 3 comma space 6 right square bracket and differentiable on left parenthesis short dash 3 comma space 6 right parenthesis. When evaluated, f left parenthesis short dash 3 right parenthesis equals 383 and f left parenthesis 6 right parenthesis equals short dash 1399. Therefore, f left parenthesis a right parenthesis not equal to f left pare