# How do you find the critical points for #x^2-5x+4# and state whether it is stable or unstable?

##### 1 Answer

The critical points of a single variable function are the points in which its derivative equals zero. If the second derivative is positive in these points, the points are unstable; while if the second derivative is negative, the points are stable.

This is a polynomial function, so the derivative of each term

So, the derivative of

The derivative of

The derivative of a constant is zero.

So, the first derivative of

The second derivative is the derivative of the derivative, and we get that the derivative of

So, the (only) critical point