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[Post New]10 Mar 2008 17:01:18 IST
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man111 (54)

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(1)   if f(x)=x8+x6-x4-2x3-x2-2x+9 than find the minimum value of f(x).
 
 
    
[Post New]10 Mar 2008 17:16:03 IST
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akhil_o (2709)

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it is clearly 5 by graph..

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[Post New]10 Mar 2008 17:35:31 IST
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man111 (54)

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how ca you say that the graph of this fuction you are sketchig is write
 
akhil can you solve this question by calculus without using graphical method.
 
 
 
i will wait ur resoponce...................... 
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[Post New]10 Mar 2008 19:03:08 IST
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hsbhatt (5581)

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\text{No calculus-valculus required}\\ \\ \text {The given expression is equivalent to} \\ \\ (x^8-2x^4+1) + (x^6-2x^3+1)+(x^4-2x^2+1)+(x^2-2x+1)+5 \\ \\ = (x^4-1)^2 + (x^3-1)^2 + (x^2-1)^2+(x-1)^2+5 \\ \\ \text {Now, it is easy to see that the minimum value is 5, attained at x=1}
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[Post New]10 Mar 2008 19:05:31 IST
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Radon222 (166)

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Oh my goodness ! Such a fine answer.
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