Let $f(x) = x^3 - 5x^2 + 1$.
Fill in the values or intervals below.
If there is nothing applicable for a given category enter NONE. For $\infty$ use infinity.
For $-\infty$, use -infinity. To indicate a union of intervals, use U.
interval(s) on which $f$ is increasing
interval(s) on which $f$ is decreasing
$x$-coordinates of all local maxima
$x$-coordinates of local minima
interval(s) on which $f$ is concave up
interval(s) on which $f$ is concave down
Use your results, as recorded above, to sketch the graph of $f$. Check by making a plot
(not submitted).