Question

Find all the critical points and local min/max.

Answer 1

\[f(x) = \frac{ x^2-6x+12 }{ x-4 }\]

\[f'(x) = \frac{ x^2-8x+12 }{ (x-4)^2 }\]

I've found the 1st derivative already but I'm not too sure about the rest. For my Critical Points I have them being 2 and 6. But I was wondering if 4 should be a critical point as well since the denominator could be (4-4)^2 = 0

Answer 2

Yes, critical points are those x values that make f'(x) = 0 or f'(x) undefined. Therefore, 2,4 and 6 are CPs.