Calculate the length of the curve y = x2 for x E [0, t]. Use this information to parametrizationve using "unit speed", and use this to calculate the curvature of this curve at every point. If this parametrization seems too difficult, try to find the osculating circle at each point (t, t2 ) by calculating the radius of a circle passing through three nearby points and then taking the limit of the expression you obtain as the three points get arbitrarily close. Even more efficiently, look at a circle tangent to the curve at (t, t2) and passing through a nearby point, then take the limit of the radius as the point gets arbitrarily close