# Fam. of func.

• Mar 27th 2008, 01:44 PM
mathlete
Fam. of func.
need some help on finding the critical value and x intercept of this equation:

y(x) = ax-xln(x)

thanksness
• Mar 27th 2008, 02:11 PM
teuthid
the x-intercept is the $x_0$ such that $y(x_0)=0$. so...

$0=ax-x\ln x$

$\rightarrow ax=x\ln x$

$\rightarrow a = \ln x$

$\rightarrow x=e^{a}$

so the x-intercept of this function is $(e^{a},0)$.

What's the definition of a critical value? I'm not familiar with that term.
• Mar 27th 2008, 05:56 PM
topsquark
Quote:

Originally Posted by mathlete
need some help on finding the critical value and x intercept of this equation:

y(x) = ax-xln(x)

thanksness

A critical value would be a value where the first derivative of the function is 0 or where the function does not exist.

So the function does not exist at x = 0, so this is a critical point.

$y^{\prime}(x) = a - ln(x) - 1$

So when this is 0 we have a critical point:
$a - ln(x) - 1 = 0$

$ln(x) = a - 1$

$x = e^{a - 1}$

So this is your other critical point.

-Dan