Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 72

Use a graphing calculuator to check the results of the function $\displaystyle y = \frac{3x^4 + 2x}{x^3 - 1}$ and its derivative
$\displaystyle y' = \frac{3x^6 - 16x^3 - 2}{(x^3 - 1)^2}$




Based from the graph, we can see that the function has a positive slope or positive derivative when it is increasing.
On the other hand, the function has a negative slope or negative derivative when the function is decreasing.
Also, the function has a zero slope at the minimum and maximum point of the graph.
Moreover, the function is not differentiable at $x=1$ because the function is undefined at that point.