1. ## 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

2. 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

3. also remember that if the factorization isnt obvious that you can always use the quadratic equation.