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