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# Maths C2 question help please watch

1. Heres the question
http://img694.imageshack.us/img694/4826/aaaaaaof.jpg
I got up to the point x>+/-2
When you draw the graph I don't get why it's the part below the X axis at -2<x<2
2. Values of x for which f(x) is an increasing function means values of x for which f'(x)>0.
3. An increasing function means .

If you find such that , then you're finding the turning points of , and due to the sign of the coefficient of the variable with highest power, we know the function overall is generally decreasing (as it's a cubic), but there'll be a part of it which is increasing, and it's increasing between the turning points.
4. Try doing a small rough sketch of what it's supposed to look like - that'll help.
5. f(x)=12x-x^3
f is derivable on R as sum of two functions derivable on R [u(x)=12x and v(x)=-x^3]
Therefore, for all x of R, f'(x)=12-3x²
f'(x)=0 <=> 12=3x² <=> x²=4 <=> x=-2 or x=2
For x<2 and x>2, f'(x)<0 so f decreasing
For -2<x<2, f'(x)>0 so f increasing

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Updated: January 14, 2010
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