quartic functions?

Question

How do I go about making a proof for the general quartic form if i start with the inflection points (the zeros of the double derivative). I know i take the antiderivative in order to get the equation, but then where do I go to find the ratios between the roots?

Answer 1

quartic function is of the type ax^4+bx^3+cx^2+dx+e

Answer 2

A quartic function is a function of the form

f(x)=ax^4+bx^3+cx^2+dx+e \,

with nonzero a; or in other words, a polynomial function with a degree of four. Such a function is sometimes called a biquadratic function, but the latter term can occasionally also refer to a quadratic function of a square, having the form

ax^4+bx^2+c \,,

or a product of two quadratic factors, having the form

(ax^2+bx+c)(dy^2+ey+f) \,.

Since a quartic function is a polynomial of even degree, it has the same limit when the argument goes to positive or negative infinity. If a is positive, then the function increases to positive infinity at both sides; and thus the function has a global minimum. Likewise, if a is negative, it decreases to negative infinity and has a global maximum.

Answer 3

The only thing I know about them is that it is a function that has x^4 in it. I don't know how to solve it. Yet...

Answer 4

And the question?


Ana