For what values of x is #f(x)=(x-3)(x+2)(x-1)# concave or convex?
1 Answer
May 27, 2018
Refer Explanation.
Explanation:
Given that:
By using second derivative test,
-
For the function to be concave downward:
#f''(x)<0#
#f(x) =(x^3-2x^2-5x+6)#
#f'(x) =3x^2-4x-5#
#f''(x) =6x-4#
For the function to be concave downward:
#f''(x)<0#
#:.# #6x-4<0#
#:.# #3x-2<0#
#:.# # color(blue)(x<2/3) # -
For the function to be concave upward:
#f''(x)>0#
#f(x) =(x^3-2x^2-5x+6)#
#f'(x) =3x^2-4x-5#
#f''(x) =6x-4#
For the function to be concave upward:
#f''(x)>0#
#:.# #6x-4>0#
#:.# #3x-2>0#
#:.# # color(blue)(x>2/3) #