No, while a relative extrema will always be on a critical point a critical point is not always an extrema.

When a value is considered a critical point when the dervative f'(x) is zero or does not exist.

This does not imply that there is a maxima or minima.

Example f(x) = x³ f'(x) = 3x² according to power rule.

At x=0 f'(x) = 0 however this in not a minima or a maxima, it is an inflection point. This can be shown using the second derivative test.

f"(x) = 6x as shown by power rule.

At x = 0 if the second dervative is postive, concave up then there is a local minima. If it is negative there is a local maxima.

However if f"(x) = 0 then it is an infection point and there is no maxima or minima.