I recently got this question in a coursework:
Find the maximum value of f(x) = 4x^2 - x^4 + 4.
For what value(s) of x does this occur.
That was the full question, it didn't state any desired method to use.
So I got: dy/dx = 8x - 4x^3
worked out that when dy/dx = 0, x=0 or +/- sqrt(2)
then I got: d^2y/dx^2 = 8 - 12x^2
so when x = 0, d^2y/dx^2 = +8, ie a minimum.
when x = +/-sqrt(2), d^2y/dx^2 = -16, ie maximum.
so I put x = +/- sqrt(2) back into the original equation to get 8.
My final answer was the maximum is 8, and this occurs when x = +/- sqrt(2).
But I only got 2 out of 4 marks. He/she (I'm not sure who marked it) put a note next to my second derivative saying that I have to evaluate them. I don't know what this means, I have evaluated the answer and surely I don't have to evaluate f(0) if I know it's a minimum.
What are your thoughts?
2007-12-07
00:17:12
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5 answers
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asked by
eazylee369
4
in
Mathematics