Ok so I am trying to do this problem and I have a question(adsbygoogle = window.adsbygoogle || []).push({});

So based on the definition given in the book "An interior point of the domain of a function f where f' is zero or undefined is a critical point of f"

This is the problem:

y = sqrt(x^2 - 1)

so

y' = x/sqrt(x^2 - 1)

to find a critical point

y' = 0

x/sqrt(x^2 - 1) = 0

x = 0

also to find the critical point we have to see if y' will be undefined at any value of x. as we can see y' will be undefined at x = 0.

so from the first condition when we solved for y' = 0, we got x = 0 and now for the second condition y' is undefined at x = 0.

So both conditions are satisfied at x = 0 so does that mean the critical point is at x = 0. In the definition it says first condition or second condition has to be satisfied. I might be reading too much into the definition.

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# Finding critical point

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