Asked by kathy
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?
Answers
Answered by
Mgraph
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)
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)
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