Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 76

Use a graphing calculuator to check the results of the function $\displaystyle f(t) = \frac{t}{5 + 2t} - 2t^4$ and its derivative
$\displaystyle f'(t) = \frac{5 -200t^3 - 160t^4 - 32t^5}{(5 + 2t)^2}$




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 maximum point of the graph.
Moreover, the function is not differentiable at $x= -2.5$ because it has a vertical tangent at that point.