For what values of $k$ is $g(x)=x^3+kx^2+x$ one-to-one? I need to find for what values of $k$ $g(x)=x^3+kx^2+x$ is one-to-one. I tried finding for what values it is strictly increasing and got the derivative to be $3x^2+2kx+1>0$, but I'm not really sure where to go from there since there are two variables.

Hints:
Your function $g(x)$, being a cubic polynomial, is one-to-one if and only if the derivative has at most one root. One root is allowed.
You can tell how many roots a quadratic equation $ax^2+bx+c=0$ has by examining its discriminant $b^2-4ac$. If the discriminant is positive, there are two roots; if zero, one root; if negative, no real roots.
So examine the discriminant of the derivative of $g(x)$. That discriminant will depend on $k$, so find which values of $k$ will make the discriminant non-positive.
