Re: finding minimum


<mathforsweta@xxxxxxxxx> wrote in message news:1132679627.949875.180180@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hello Everyone,
>
>
> I have m=min(a,1/2a)..I want to find the largest of m.
>
> I differentialted 1/2a with respect to a and set it equal to zero. That
> is what we do when we want to find maximum or minimum.

I guess you mean 1/(2 a), sometimes also written as 1/(2*a)

>
> the true answer is a=1/sqrt(2)
>
> May be I am doing something wrong?
>
> Can somebody please help me with this problem?

For obvious reasons only looking at positive values
of x, the function
y = x
is monotonously increasing starting at 0 and 'going
to infinity', and the function
y = 1/(2 x)
is monotonously decreasing starting 'at infinity' and
'going to 0'.
So the minimum of the two starts at 0, follows the
line of y = x, increasing up to a certain value, until
it meets the curve of y = 1/(2 x) where it starts
decreasing again.
So you are looking at the intersection point of the
two lines.
hth.

Dirk Vdm


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