Fam. of func.

**mathlete** · March 27th 2008, 12:44 PM

need some help on finding the critical value and x intercept of this equation:

y(x) = ax-xln(x)

thanksness

**teuthid** · March 27th 2008, 01:11 PM

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.

**topsquark** · March 27th 2008, 04:56 PM

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

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