$f(x)=x^3-9x^2+24x-10$

Find the critical numbers, the local minima, and the local maxima of $f.$ You may use the second derivative test to identify local minima and local maxima$\mathrm{.}2.$b Determine the interval$($s$)$ in which $f$ is increasing and decreasing

$2.$c Find the interval in which $f$ is concave upward and concave downward

$2.$d Find the inflection point$($s$)$ of $f$