Use values of f'' to determine the concavity of the graph of f.

Determine the interval(s) over which the graph of y = 5x - X is concave up or concave down. a.) Concave up on ( - co,0) U (0,5) O Concave down on (5,co) b.) Concave up on ( - co,0) O Concave down on (0,1) U (1,90) c.) Concave up on ( - co, - 1) U(0,90) O Concave down on (- 1,0) d.) Concave up on ( - co, - 1) O Concave down on ( - 1,0) U(0,oo)- 10 g * 0, 50, X 3 + X 3 = 0. 5 X 3 ( 1 + X ) = 0. 4 X 3 + 0 if g 4 X 3 = 0 7 X = -1. X -Z for any X this is not happen Absurd result. So , The point of inflection is -1. For concave upward, dy dx ? X 3 ( x + 1 ) >0 . X 3 ( x +1 ) co . 4 Xtico M. X 3 = 3 X 0 . ] For concave downward. dy 10 * 3 ( x + 1 ) co . 9 g 10 X 3 ( X+1) >0. as . x 3 7 0 7 x +1>0. -> > >- 1 . .. So , X E ( - 1, 00 ). but at X = 0 , 10 x 3 ( x+1 ) does not exist. So , xe (- 1 10 ) U(010)