Cal question first derivative

Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point. Let
f(x) = {4/4)x^4+(8/3}x^3+{-4/2}x^2 - 8 x

There are three critical points. If we call them c_1,c_2, and c_3, with c_1 c_1 =
c_2 =
and c_3 = .

diff((4*(1/4))*x^4 + (8/3)*x^3 - (4*(1/2))*x^2 - 8*x, x) = 4*x^3 + 8*x^2 - 4*x - 8

factor(4*x^3 + 8*x^2 - 4*x - 8 = 0)

(x - 1)*(x + 2)*(x + 1) = 0

x - 1 = 0, x1 = 1

x + 2 = 0, x2 = - 2

x + 1 = 0, x3 = - 1

f(x):=(4/4)*x^4 + (8/3)*x^3 + (-4/2)* x^2 - 8* x

f(1) = - 19/3

point(1; - 19/3) = Minimum

f(-2) = 8/3

point(- 2; 8/3) = Minimum

f(-1) = 13/3

point( - 1; 13/3) = Maximum

( - ∞; - 2) = decreasing

( - 2; - 1) = increasing

( - 1; 1) = decreasing

> 1 = increasing