Critical points are important in calculus because they help us find relative maxima and minima of a function. A critical point of a function is a point where the derivative of the function is either zero or undefined. The geometric interpretation of what is taking place at a critical point is that the tangent line is either horizontal, vertical, or does not exist at that point on the curve.

To find the critical points of a function, we need to follow these steps:

1. Find the derivative of the function.
2. Set the derivative equal to zero and solve for x.
3. Determine if the critical point is a relative maximum, relative minimum, or neither by using the second derivative test or by analyzing the behavior of the function around the critical point.

It is important to note that not all functions have critical points. For example, a linear function like f(x) = 3x + 7 has no critical points.