so i am in precalculus, we need to graph the fuction using derivatives, maxima, intercepts and concavity. I am having trouble factoring cubics: for example: x^4-4x^3+16x -- x(x^3-4x^2+16)Now what? That is without calculator, how do you find the roots?

Question

so i am in precalculus, we need to graph the fuction using derivatives, maxima, intercepts and concavity. I am having trouble factoring cubics: for example: x^4-4x^3+16x --> x(x^3-4x^2+16)Now what? That is without calculator, how do you find the roots?

Mgraph · Answer

The equation x^3-4x^2+16=0 has 1 real root x=-1.68 (approx) (x^4-4x^3+16x)'=4x^3-12x^2+16=4(x^3-3x^2+4)=4(x+1)(x^2-4x+4)=4(x+1)(x-2)^2 (x^4-4x^3+16x)''=12x^2-24x=12x(x-2)