# Critical vs stationary point

1. Oct 11, 2015

### goldfish9776

1. The problem statement, all variables and given/known data

the critical point is the point which the f'(c) = 0 or f'(c) = doesnt exist . How if I'm asked to find the stationary point .

In this question , the critical point is x=0.071 , -14.071, 3 , and -2

So, if i am sked to find the stationary point , it should be only x=0.071 , -14.071 , am i right ? x=3 and -2 are excluded ?
2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### IMG_20151011_124811.jpg
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2. Oct 11, 2015

### Daeho Ro

Yes. What do you think about the reason?

3. Oct 11, 2015

### Ray Vickson

The attachment is incorrect: the function
$$f(x) = \frac{x^2+1}{x^2-x-6}$$
can be re-written as
$$f(x) = \frac{x^2+1}{(x+2)(x-3)}$$
Your attachment says that $f(-2)$ and $f(3)$ exist, but that is nonsense: you would be dividing by zero in both cases.

BTW: please refrain from using such attachments---just type things out. I find that when I open your attachment, I have no way of getting back to PF: I need to log off then log back on again.