Finding Stationary Points of a Function

[goldfish9776]

Homework Statement

the critical point is the point which the f'(c) = 0 or f'(c) = doesn't 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 ?

Homework Equations

The Attempt at a Solution

 

[Daeho Ro]

Yes. What do you think about the reason?

 

[Ray Vickson]

Homework Statement

the critical point is the point which the f'(c) = 0 or f'(c) = doesn't 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 ?

Homework Equations

The Attempt at a Solution

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.