Calculus 12 Intervals of Increase and Decrease; Concavity Worksheet . : 1. In the diagram below, find the largest open intervals over which f is: (a) increasing (b) decreasing TABLE (c) concave up (d) concave down + 2. Find all values of x where f has an inflection point. + 2 @ x=0 @ * = 2 In the following exercises, find open intervals on which f is (a) increasing (b) decreasing (c) concave up crease ! (d) concave down and (e) all inflection points ecrease : J b/c 3 . f (x ) =x2 - 5x+6 4 . f (x ) = 4-3x -x2 or 5 . f ( x ) = (x + 2 ) 3 6. f(x) =5+12x-x3 7. f(x) =3x3 - 4x+3 8. f(x) = x4 - 8x2+ 16 9. f (x ) = 3x4 - 4x3 10. f (x ) = - X x 2 + 2 1 1. f (x) = cosx, 0 0 for x 2 ( c ) f ( 2 ) = 4, f" ( x) > 0, for x # 2 and lim f'(x) = - 00, lim f'(x)= too x -+ 2