[tex]\bf f(x)=4x^3-36x^2+5\implies \cfrac{df}{dx}=12x^2-72x\implies \stackrel{\textit{setting the derivative to 0}}{0=12x(x-6)} \\\\\\ x= \begin{cases} 0\\ 6 \end{cases}[/tex]
so we have those critical values, which gives us the intervals of (-∞, 0] , [0, 6] and [6, +∞).
where is it increasing or decreasing? well, that's just a matter of checking a value on each region for the the first derivative, namely the first derivative test.
we can check for f(-1) = 12(-1)² - 72(-1), is a positive value, increasing.
and check f(1) = 12(1)² - 72(1), is a negative value, decreasing.
and check f(7) = 12(7)² - 72(7), positive, so increasing.
check the picture below, and you can see there which are the minima or maxima.
