How do you verify whether rolle's theorem can be applied

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f(x,y)=x^3-6xy+8y^3$

$\frac{1}{\sec <!--\; \; -->(x)}$ in derivative?

What is the derivative of ${\displaystyle \ln (x+1)}$?

What is the limit of ${\displaystyle e^{-x}}$ as ${\displaystyle x\to \infty }$?

What is the derivative of ${\displaystyle f\left(x\right)=5^{\ln x}}$?

What is the derivative of ${\displaystyle e^{-2x}}$?

How to find ${\displaystyle lim\frac{e^t-1}{t}}$ as ${\displaystyle t\to 0}$ using l'Hospital's Rule?

What is the integral of ${\displaystyle \sqrt{9-x^2}}$?

What is the derivative of ${\displaystyle f\left(x\right)=\ln \left[x^9{(x+3)}^6{(x^2+7)}^5\right]}$ ?

What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?

How to find the derivative of ${\displaystyle y=e^{5x}}$?

How to evaluate the limit ${\displaystyle \frac{\sin \left(5x\right)}{x}}$ as x approaches 0?

How to find derivatives of parametric functions?

What is the antiderivative of ${\displaystyle -5e^{x-1}}$?

How to evaluate: indefinite integral ${\displaystyle \frac{1+x}{1+x^2}dx}$?