What are the values and types of the critical points, if any, of #f(x) =x^3 + 3x^2-24x#?

1 Answer
Leland Adriano Alejandro
Jan 17, 2016

#(2, -28)# Minimum Point,
#(-4, 80)# Maximum Point and #(-1, 26)# Point of inflection

Explanation:

#f(x)=x^3+3x^2-24x# the given
#f' (x)=3 x^2 +6 x-24# the first derivative

Let #f' (x) = 0#
#3 x^2 +6 x-24=0#
solving for x:
#x=2# and #x=-4#
when #x=2# , #y=-28# Minimum point
when #x=-4#, #y=80# Maximum Point

Solving for #f'' (x)#
#f'' (x)=6x+6#
set #f''(x)=0# and solving for x:
#6x+6=0#
#x=-1#
when #x=-1#, #y=26# Point of inflection

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