1. ## minimum value

Find the value of p which makes the value of p + 1/p a minimum

Find the value of p which makes the value of p + 1/p a minimum
I would attempt it like this:

let $\displaystyle f(p) = p + \frac{1}{p}$

$\displaystyle f'(p) = 1 - \frac{1}{p^2}$

for stationary point let $\displaystyle f'(p) = 0$

this implies that $\displaystyle \frac{1}{p^2} = 1$

so $\displaystyle p = \pm 1$

3. Originally Posted by U-God
I would attempt it like this:

let $\displaystyle f(p) = p + \frac{1}{p}$

$\displaystyle f'(p) = 1 - \frac{1}{p^2}$

for stationary point let $\displaystyle f'(p) = 0$

this implies that $\displaystyle \frac{1}{p^2} = 1$

so $\displaystyle p = +/- 1$
Just a friendly suggestion.

You can generate the plus or minus sign in LaTeX, using the command \pm. It yields $\displaystyle \pm$

You can also generate a minus or plus sign in LaTeX, use the command \mp. It yields $\displaystyle \mp$.

--Chris

If $\displaystyle p>0$ then:
$\displaystyle p+\frac{1}{p} \geq 2\left( p \right)\left( \frac{1}{p} \right) = 2$ by AM-GM.
Now for $\displaystyle p=1$ we have a minimum.