# Critical number?

• Dec 9th 2008, 05:29 PM
DHS1
Critical number?
Determine all of the critical numbers of the given function.

I'm like 90% sure that means solve for x, check if what you got for x actually works, and that/those are your critical number(s).

Anyways, here's the problem:

$g(x) = x - \sqrt{14-x} - 2$

Any ideas anyone? I tried solving for x:

$0 = x-\sqrt{14-x} - 2$

then
$\sqrt{14-x} = x-2$

then squared both sides
$14-x = x^2-4$

then moved some stuff around
$18 = x^2+x$

and now I'm stuck there, not even knowing if I'm supposed to be doing this.

HALP
• Dec 9th 2008, 05:46 PM
skeeter
Quote:

Originally Posted by DHS1
Determine all of the critical numbers of the given function.

I'm like 90% sure that means solve for x, check if what you got for x actually works, and that/those are your critical number(s).

Anyways, here's the problem:

$g(x) = x - \sqrt{14-x} - 2$

Any ideas anyone? I tried solving for x:

$0 = x-\sqrt{14-x} - 2$

then
$\sqrt{14-x} = x-2$

then squared both sides
$14-x = x^2-4$ ... mistake here, corrected below

$14 - x = x^2 - 4x + 4$

$0 = x^2 - 3x - 10$

$0 = (x - 5)(x + 2)$

$x = 5$ ... $x = -2$

check both solutions in the original equation
• Dec 9th 2008, 06:08 PM
Mentia
also remember that if the factorization isnt obvious that you can always use the quadratic equation.