Question

Question

Answer 1

Do critical numbers include any values where f(x) or f'(x) is undefined ?

Answer 2

@aum

Answer 3

Lets say I am given that:
\[f'(x)=\large \frac{x^2-1}{x^2+2x-3}\]

Answer 4

So would the critical numbers include 3 and -1 ?

Answer 5

I believe not. If x = -1, then the function is undefined.

Answer 6

So -1 and 3 are or are not included among the critical numbers (which I would find by setting f'(x)=0 and solving for x) ?

Answer 7

This is the question I am asking. Do critical numbers include undefined values?

Answer 8

No. http://tutorial.math.lamar.edu/Classes/CalcI/CriticalPoints.aspx
Here it says "Again, remember that while the derivative doesn’t exist at and neither does the function and so these two points are not critical points for this function."

Answer 9

yes

Answer 10

I just found that wherever C at which f'(x) is undefined is a critical number IFF C is in the domain of the f(x).

(And not a critical number IFF C is not part of the domain of f(x) )

Answer 11

tnx