Show that the curvature is greatest at the endpoints of the major axis, and is least at the endpoints of the minor axis, for the ellipse given by $\displaystyle x^2 +4y^2 = 4$

To solve this problem, do I need to compute $\displaystyle K = \frac{|y''|}{[1+(y')^2]^{3/2}}$; and then find $\displaystyle \frac{dK}{dx}$, to determine if the critical values coincide with the end points of the ellipse?