Question

Consider the function f(x) = 4(x - 2)2/3. For this function there are two important intervals: (- 00, A) and (A, 0c) where A is a critical number. Ais For each of the following intervals, tell whether f(x) is increasing or decreasing. (-0, A): Select an answer v (A, 0): Select an answer v For each of the following intervals, tell whether f(x) is concave up or concave down. (- 00, A): Select an answer (A, 00): Select an answer

Answer 1

solution fex) = 4 (x-2) Note: Critical points of function fex) are either roots of f(x) = 6 feas not exists at that point Now, f(x) = 4X 2 (x-23737 (x-2) 8 3 8 3 Now 3x6 R sit. fcx) =0 But at fcas not exists 2 2 is critical point of feas, A = 2 O now for a 22 f'cas co fer a> 2 8 (-00, 2) : fex decreasing (2,00) o fex) increasing.

I cx) = 8. 1 (2-2) % f"ca) - 2 Now, -8 (2-2) 9 Now, for x 22 f'ca) Lo also for x 2 Ta zo concave down C-002) : fox) (2100) : fcx) Coneave down