f(x) = 3x^4 - 8x^3 + 6x^2 Find the derivative of the function
f'(x) = 12x^3 - 24x^2 +12x The critical values are the f' set = 0
12x^3 -24x^2 + 12x = 0
12x(x^2 - 2x + 1) = 0 factor out 12x
12x (x - 1) (x - 1) = 0 factor the x^2 factor
12x = 0 , x - 1 = 0
x = 0 , x = 1
restating the f'
f'(x) = 12x^3 - 24 x^2 + 12x find the second derivative
f"(x) = 36x^2 - 48x + 12
f"(0) = 12 positive that means there is a min at x = 0.
f"(1) = 36(1) - 48(1) + 12 = 36 -48 + 12 = 0 at x = 1 there is a invertion point.