SOLUTION: Help! How do you factor: -4x^3+36x^2-12? It is the prime of f(x)=12x^3-12x+24. I need to find the intervals where the graph of f is concave upward, concave downward and the infle

Question 1826: Help! How do you factor: -4x^3+36x^2-12? It is the prime of f(x)=12x^3-12x+24. I need to find the intervals where the graph of f is concave upward, concave downward and the inflection points.
Thanks,
Anne

Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
i would do this by calculus...
dy/dx = = 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...

cheers
Jon.
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