Question

(1 point) Consider the function f(x) = x2/5(x – 9). This function has two critical numbers A< B Then A = and B For each of the following intervals, tell whether f(x) is increasing or decreasing. (-0, A]: ? [A, B]: ? [B, 0) ? The critical number A is ? and the critical number B is ? There are two numbers C < D where either F"(x) = 0 or f'(x) is undefined. Then C= and D= Finally for each of the following intervals, tell whether f(x) is concave up or concave down. (-0, C): ? (C,D) ? (D, ) ?

Answer 1

215 (2-0) 2 3 215 m/h x 1+(«-9). 2.2 5 t'(x)=x → 4x)= a 215 t 2 (2-a) 5 x 35 의 scal 52 + 2X-18 52315 t'l (20 = 72-18 315 52 f'(x) is undefined at a=o = 0 And t'ia 7x-18 52315 8 کی -> 776-18 so x = long '- the two emitteal numbers are x=0&x= Then A=0 and B = ola 18 7

sign of f'ra fon diffenent Values of x. at 16 fox) is in ere ineneating and flag is dec on (-4,000 (18.) deenenting on (0,4). Now f'cao 295.7–1782-18).1.2-25 - Glt (x315)? 7x the 315-173-18) 2215 bis х 212+54 z of 3 52 52 815 f'(a) 14x+54 252815 f"(x) is undefined at =0 f'(x) 148+52 252/5 = 0 =) 14x+56=0 54 14 7 x = 27 / and D = Then c= - 2 / 2 sign of f'(x) for different values of a. A ~ -27 27 Concare up on i fires is on (21,09 010,00) and feas is concave down on (-4,-27 )