Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point. Let
$f(x) = \frac{5}{4}x^4+\frac{10}{3}x^3+\frac{-5}{2}x^2 - 10 x$

There are three critical points. If we call them $c_1,c_2,$ and $c_3$, with $c_1<c_2<c_3$, then
$c_1$ =
$c_2$ =
and $c_3$ = .

Is $f$ a maximum or minumum at the critical points?
At $c_1$, $f$ is ? Local Max Local Min Neither
At $c_2$, $f$ is ? Local Max Local Min Neither
At $c_3$, $f$ is ? Local Max Local Min Neither

These three critical give us four intervals.
The left-most interval is , and on this interval $f$ is ? Increasing Decreasing while $f'$ is ? Positive Negative .
The next interval (going left to right) is . On this interval $f$ is ? Increasing Decreasing while $f'$ is ? Positive Negative .
Next is the interval . On this interval $f$ is ? Increasing Decreasing while $f'$ is ? Positive Negative .
Finally, the right-most interval is . On this interval $f$ is ? Increasing Decreasing while $f'$ is ? Positive Negative .