To answer this, find the 1st and 2nd derivatives of f(x)=x^4-5x^2+4:
f '(x) = 4x^3 - 10x and f "(x) = 12x^2 - 10
Set f '(x) = 2x(2x^2 - 5) = 0 and solve for the critical values: There are 3: {0, +sqrt(10)/2 , -sqrt(10)/2}. Please see the remainder of my response, below.