Final answer:
The curvature of the function y=√3x is 0. The radius of curvature at x=3 is undefined. There is no center of curvature.
Step-by-step explanation:
The curvature of a function can be found using the formula k = |y''| / (1 + (y')²)^(3/2), where y' denotes the first derivative and y'' denotes the second derivative of the function. In this case, the function is y = √3x. Taking the first derivative of y, we get y' = √3. Taking the second derivative of y, we get y'' = 0. Therefore, the curvature k = 0 / (1 + (√3)²)^(3/2) = 0.
The radius of curvature at x = 3 can be found using the formula r = 1/k, where k is the curvature. Since the curvature in this case is 0, the radius of curvature at x = 3 is undefined.
The center of curvature is the point on the curve that is equidistant from the curve at two points. Since the radius of curvature is undefined at x = 3, there is no center of curvature.