Question

Consider the function below. h(x) = (x + 1)3 - 3x - 2 (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (c) Find the inflection point. (x, y) = ,Y)=([ Find the interval where the graph is concave upward. (Enter your answer using interval notation.) Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

Answer 1

fra) (x+y) - 3x * s'(x) = 3x² +62 f'(x) = 6x + 6 Critical found $'(X) = 0 3x² +6x=0 3x(2+2).O X-2 domain -00 CZ-? -2<xco, Check sign of fou at xs-3 F-3) = 9 (-00,-2) » Take (-2,0) & Take (tve) to) --3 love) (o, o) Take No t') : 9 (ave) flas increases 6-00,-2) 0 (0.00) (-2,0) f(x) decreases » b) at mininum mininum value & f(0) = at x = -2 is maximum a maximum value f(-2) 3 c) Inflection f'(X) =0 6x+6=0 . f(-) (2,4). SC-1 )

-00 < x < -1, -ICXCOC Check sign af f(as at C-ve) (roo,-1) - f''(-2) = -6 Take xa - 2 ( -o) z Take x = 6 > filos? 6 (avel Con Cave upward » (-1,00) Con Cave downward as (-co, a")