Take the polynomial function fxx310x What is the end behavio

Take the polynomial function f(x)=x^3-10x. What is the end behavior of the function?

f(x)-->_____ , as x---> negative infinity

f(x)-->_____ , as x--> positive infinity

What are the zeros of the function?

Enter your answers as exact simplified solutions seperated by commas. Do not approximate.

x=_______

Solution

f(x) = x^3 -10x

ax x ---> -infinity;

f(x) = (-x)^3 +10x ;f(x) ----> -infinity

f(x) = x^3 -10x

as x --->+ infinity

f(x) ----> + infinity

Zeros of f(x) : f(x) =0;

x^3 -10x =0 ---> x(x^2 -10) =0

x = 0 , x = +/sqrt(10)

Zeros of f(x): x =0, sqrt10 , -sqrt10