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Maxima and Minima of a function 
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#1
Jan909, 11:26 PM

P: 265

Are there any analytical techniques to do this besides the Derivative Test?



#2
Jan1009, 06:34 AM

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P: 39,557

There is no general method except by checking where the derivitive is 0 (or does not exist). For some functions, there are other ways. For example we can always find minima and maxima for quadratic functions by completing the square.



#3
Jan1009, 12:27 PM

P: 265

I see. Thanks for that.



#4
Jan1109, 07:53 AM

P: 32

Maxima and Minima of a function
But there is also possibility to estimate. If you solve some elementary function, for example:
[tex]f(x)=x^2+3x+2[/tex] You can transform it to form: [tex]f(x)+\frac{1}{4}=\left(x+\frac{3}{2}\right)^2[/tex] So now you are able to find a minimum: [tex]\min_{x\in\mathbb{R}}f(x)=\frac{1}{4}[/tex] 


#5
Jan1109, 03:05 PM

P: 265

Yes, but my function is far too complex/tedious to do either way. An expression for the min and max has been found though proving it is too difficult for me.



#6
Jan1109, 03:21 PM

P: 626




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