Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 64

Use a graphing calculuator to check the results of the function $\displaystyle g(x) = \frac{3x^7 - x^3}{x}$ and its derivative
$g'(x) = 18x^5 - 2x$




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.