1. {18 Points] DETAILS MY NOTES Find the critical numbers of the function f(x) = x2/3(7 x) and then use a Maple graph of the function to determine if each critical number denes a local maximum or local minimum of the function or neither. (If an answer does not exist, enter DNE.) smaller value x ---Select v larger value x = ---Select-- v 2. {116 Points] DETAILS MY NOTES Find the critical numbers, if any, of the function f(x) = 3x5 50x3 + 135x +15 and then use a Maple graph of the function to determine if each critical number denes a local maximum or local minimum of the function or neither. (If an answer does not exist, enter DNE.) smallest value x = Select--- v X = -Select-- v X = Select--- v largest value x = Select--- v 3. [l8 Points] DETAILS MY NOTES Find the global minimum and maximum of the continuous function f(x) = on {1, 2], xz+1 global minimum value global maximum value 4. [l8 Points] DETAILS MY NOTES Find the global minimum and maximum of the continuous function f(x) = x3 3x+ 7 on [0.2]. global minimum value global maximum value 5. [l8 Points] DETAILS MY NOTES Find the global minimum and maximum of the continuous function f(x) = x2 8 ln(x) on [1,4], (Round your answers to two decimal places.) global minimum value global maximum value . [l6 Points] DETAILS MY NOTES 4 Show that the function f(x) = 2 4 has an absolute maximum but not an absolute minimum. x + 4 4 0 for all x E IR. Since lim = |:| fdoes not take on an absolute minimum. X2+4 xaoox2+4 f(x) = 4 Since x2 + 4 a 4, it follows that f(x) = 1' f(0) = :l and that is the absolute maximum. x2+4