QUESTION 01

Determine if the requirements for Rolle's theorem are met by the function f(x) = - on the interval [ - 3, 3] . If so, find the values of cin (-3, 3) guaranteed by the theorem. f(x) is continuous on [-3, 3] and differentiable on (- 3, 3) . When evaluated, f( - 3) = and f(3) = . Therefore, f(a) =f(b) and the conditions of Rolle's theorem are met. The value guaranteed by Rolle's theorem is c = 0 . f(x) is not continuous on [- 3, 3] . Therefore, the first O requirement is not met and Rolle's theorem does not apply.f(x) is continuous on [- 3, 3] but not differentiable on ( - 3, 3) O . The conditions of Rolle's theorem are not met. f(x) is continuous on [- 3, 3] and differentiable on (- 3, 3) . O When evaluated, f( - 3) = - and f(3) = . Therefore, f(a) = f(b) and the conditions of Rolle's Theorem are not met.Identify all of the global and local extrema of the graph. 5 2 1 -2 -1 0 3 5 6 6 5 -3 2 12 -3 -40 is a global and local maximum of f(x) at x = 0. -0.8 is a local minimum of f(x) at x =2 . -5 is a global minimum of f(x) at x = - 1 . 0 is a global maximum of f(x) at x =0 . O -5 is a global minimum of f(x) at x = - 1 . 0 is a global and local maximum of f(x) at x =0 . O -5 is a global minimum of f(x) at x = - 1 . 0 is a global and local maximum of f( x) at x =0 . O -5 is a global and local minimum of f(x) at x = - 1