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April 21st, 2012, 11:54 PM   #1
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minimum value of function

The minimum value of f(x)=x^8+x^6-x^4-2x^3-x^2-2x+9 is:
a 5
b)1
c)0
d)9
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April 22nd, 2012, 12:15 AM   #2
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Re: minimum value of function

If im not misunderstanding you, then the answer is d) , 9
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April 22nd, 2012, 12:22 AM   #3
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Re: minimum value of function

The derivative of f equated to zero has only 1 real root, which is .

meaning there is a minimum there and since f has an even order, we know this is a global minimum.

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April 22nd, 2012, 12:25 AM   #4
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Re: minimum value of function

Quote:
Originally Posted by MarkFL
The derivative of f equated to zero has only 1 real root, which is .

meaning there is a minimum there and since f has an even order, we know this is a global minimum.

Thanks. The problem I was facing was with finding the roots of the first derivative. Can u please explain how u have found that? Thanks again
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April 22nd, 2012, 12:39 AM   #5
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Re: minimum value of function

I used the rational roots theorem, and checked, using polynomial division to find:



I then found numerically that the remaining 6th order factor has a global minimum greater than zero, hence it has no real roots.
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