Required Given the graph of f'(x), sketch a possible graph of f(x). AS' ( x ) 8 6 2 A f(x ) O 18 x O A f(x) O O2 Required Given the graph of f(x), sketch an approximate graph of f'(x). A f( x) X O 8 x Af' ( x ) O x AS '( x ) O AS ( x)Required Find the x-coordinates of all critical points and find the open intervals where the function is increasing and decreasing. y =-x' - 8x2 - 21x - 21 Critical points at: x = -12, - 28 O 3 Increasing: -12, - 28 3 Decreasing: (-co, -12), - 28 Critical points at: x =-1, - 9 O Increasing: (-co, -1), - . . Decreasing: (-1, - ,) Critical points at: x = -3, -- 3 O Increasing : (- 3 , - Decreasing : ( - co , - 3 ) , (- 3 , 0. No critical points exist. Increasing: (-co, -3), 0. Decreasing: -3, - -4 Required Find all points of relative minima and maxima. f (x ) . 4x x' +4 8 Relative minimum: -8, 17 O 8 Relative maximum: 18, 17 O Relative minimum: (- 2 , -1) Relative maximum: (2, 1) O No relative minima. No relative maxima. Relative minimum: WIN O WIN Uilw Relative maximum:5 Required Given the graph of f(x), sketch an approximate graph of f"(x). A f( x ) 6 4 -2 AS" ( x ) O AS" ( x ) O $ Af" ( x ) O ORequired V Find the x-coordinates of all points of inflection and find the open intervals where the function is concave up and concave down. y=-x' + 4x2 - 3 No inflection points exist. Concave up: 4 3 , .. Concave down : ( - co , ) Inflection point at: x = O Concave up: -co, ~ Concave down: W/A Inflection point at: x = O Concave up: -0o, 16 3 Concave down: 3 Inflection point at: x = O Concave up: co| Concave down: -0o, a