Consider the function f(x) = 12 x^5 + 75 x^4 - 120 x^3 + 6.?

Question

For this function there are four important intervals: (-\infty, A], [A,B],[B,C], and [C,\infty) where A, B, and C are the critical numbers.

Find A, B, and C
At each critical number A, B, and C does f(x) have a relative min, a relative max, or neither?
A=
B=
C=

Answer 1

The Critical numbers are -6,0 and 1 as they are the roots of
60x^2(x^2+5x+6)=0
The sign of the derivative is

+++++++(-6)-------(0)----(1)++++
lAt x=-6 local max.
At x=0 (nothing)
At x=1 local min.

Answer 2

a=5 b= 12 c=35 fx relative max