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.

if the derivative had two roots, for $y$ between the local max and local min there would be three values of $x.$ you must require the discriminant $$k^2 - 3 \le 0$$ that means $$-\sqrt 3 \le k \le \sqrt 3. $$
