The curvature of a function h(x) at a point is the reciprocal of the radius of the circle that best approximates the shape of the function at that point. It is given by the following formula:

= (|h (x)| ) / (1 + [h (x)]^2)^ 3/2

Find the curvature, in exact and approximate form, of the following functions at the given points. (Remember that you can use Rational(3,2) to get the exact value of 3/2 . Just dividing 3 by 2 gives a floating point.)

(a) h(x) = x^2 + 3x + 5 at x = 2

(b) h(x) = tan(x) at x = /3

(c) h(x) = 7x 1 at x = 5

(d) h(x) = (25 x^ 2) at x = 1

(e) In a print statement, give a geometric relationship between the answers to (c) and (d) and characteristics of those curves.