Which of the following best describes the end behavior of the function $f\left(x\right)=2x^3-3x^2-3$?

For the curve $y=1+40x^3-3x^5$, at which point does the tangent line have the largest slope?

Consider the function $q\left(x\right)=54x^4+125x$. What are the critical numbers of $q\left(x\right)$?

Suppose the graph of $f\left(x\right)$ is shown below. At which intervals is $f^{\prime }\left(x\right)$ $<0$?

Suppose the graph of $f\left(x\right)$ is shown below. At which of the following intervals is $f^{″}\left(x\right)$ $>0$?

For which values of $x$ is the function $f\left(x\right)=(x^2-3)e^{-x}$ increasing?

Consider the following graph of $f\left(x\right)$. Which of the following points are inflection points of $f$?

Let $f\left(x\right)=x^3+a{x}^2$. For what value of $a$ does $f\left(x\right)$ have a critical point at $x=1$?

For the curve $y=5\ln \left(x\right)$, at what point does the curve have maximum curvature?