When using the first derivative test to find the critical points of a function, do you always have to include x=0?

1 Answer
Feb 11, 2017

Yes, if 0 is in the function's domain. Note that if the derivative isn't defined at 0, that is also a critical point.

Explanation:

That is because 0 can be a critical point of a function. For example, consider the function f(x) = x^2.

f'(x) = 2x, and the root to the equation f'(x) = 0 => 2x = 0 is

x = 0.

At 0, our f also happens to have an absolute minimum, which wouldn't always be the case.

In fact, many such situations exist, so, unless 0 is not in the functions domain, there is no reason why you wouldn't check what happens there.