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.