Question 1826
i would do this by calculus...

dy/dx = {{{-12x^2 + 72x}}} = 0
so x=0, x=6 are the 2 turning points

when x=0 then y=-12
when x=6 then y=420

d2y/dx2 = -24x + 72

when x=0, this is positive therefore a MIN
when x=6, this is negative therefore a MAX

Ask yourself also the following:

when x is a HUGE -ve number, what will y be?...here the cube power will dominate, so a cube of a negative number is negative but then there is a negative in front of the cube term too...so y will be hugely postive.

when x is a HUGE +ve number...the cube will be a huge +ve number then there is the negative sign in front...so y will be hugely negative

Now armed with this knowledge, sketch the graph, so you can see it and then you can answer where does it increase or decrease...


{{{graph(300,300,-5, 12, -50, 500, -4x^3 + 36x^2 - 12)}}}



cheers
Jon.