Identify all of the global and local extrema of the graph. -6 -5 + -3 y 5 11 10 9 00 7 6 W 4 3 2 O -1 2 3 A 5 6 X 11 is a global maximum of f(x) at x = -3. 3 is a global and local minimum of f(x) at x = -1 and x = 1. 11 is a global maximum of f(x) at x = -3. O3 is a global and local minimum of f(x) at x = -1 and x = 1. 5 is a global and local maximum at x = 0. 11 is a global maximum of f(x) at x = -3. O 3 is a global and local minimum of f(x) at x = -1 and x = 1. 5 is a local maximum at x = 0. 11 is a global and local maximum of f(x) at x = -3. 3 is a local minimum of f(x) at x = -1 and x = 1. 5 is a global and local maximum at x = 0. Determine if the requirements for Rolle's theorem are met by the function f(x)=x-3x+10 on the interval [0, 3]. If so, find the values of c in (0, 3) guaranteed by the theorem. f(x) a polynomial so it is continuous on [0, 3] and differentiable on (0, 3). By Rolle's theorem, the value is c = -3. O f(x) is not continuous on [0, 3] so Rolle's Theorem cannot be applied. O f(x) is a polynomial so it is continuous on [0, 3] but f'(x) is not differentiable on (0, 3); therefore, Rolle's Theorem cannot be applied. f(x) is a polynomial so it is continuous on [0, 3] and differentiable on (0, 3). When evaluated, f(0) = 10 and f(3) = 10. Therefore, f(a) = f(b) and the conditions of Rolle's theorem are met. The value guaranteed by Rolle's theorem is c = 3 2 Evaluate the following limit: lim O O 3x im (2x-1) - 2 = e x lim (x - 1)= = 2x lim x 3x 2x 3x (x = 1) x = - 2/12 3 2x 3x & 4m (2x-1) x X lim (2x-1) - 2/ 3x 3 = X Evaluate lim - 3 - 3x +8 X-4 X-4 Does not exist - by graphing.