What are the points of inflection of #f(x)= x^3 - 12x^2 + 2x + 15x #?

1 Answer
Nov 16, 2016

# "(4 , -30)" # is the inflection point.

Explanation:

Determining the points of inflection is by finding the second
#" "#
derivative then solve the equation for #f''(x)=0#.
#" "#
#" "#
#f'(x) = 3x^2 - 24x + 2 + 15#
#" "#
#f''(x) = 6x -24#
#" "#
#" "#
#f''(x) = 0#
#" "#
#6x -24 = 0#
#" "#
#rArr 6x = 24#
#" "#
#rArr x = 24/6 = 4#
#" "#
#" "#
Finding its ordinate #f(4)#.
#" "#
#f(4) = 4^3 - 12(4)^2 + 2(4) + 15(4)#
#" "#
#f(4) = 64 - 192 + 8 + 90#
#" "#
#f(4) = -30#
#" "#
#" "#

Hence, # "(4 , -30)" # is the inflection point.