Determine how many, what type, and find the roots for f (x) = x^3 - 5x^2 - 25x + 125

X^3-5x^2-25x+125

(x^3+125) - 5x^2-25x

(x+5) (x^2-5x^2+25) - 5x^2-25x

(x+5) (x^2-5x^2+25) - 5x (x+5)

(x+5) (x^2-5x+25-5x)

(x+5) (x^2-10x+25)

(x+5) (x-5) (x-5)

x = - 5 and 5

So there are two roots when x = ±5

df/dx=3x^2-10x-25

d2f/dx2=6x-10

So when x=-5, acceleration is negative and this is a local maximum for f (x) and when x=+5, acceleration is positive and this is a local minimum for f (x).