Consider the function (x) = x 4 - x. (a) Use a computer algebra system to find the curvature K of the curve as a

Consider the function ƒ(x) = x⁴ - x².

(a) Use a computer algebra system to find the curvature K of the curve as a function of x.

(b) Use the result of part (a) to find the circles of curvature to the graph of ƒ when x = 0 and x = 1. Use a computer algebra system to graph the function and the two circles of curvature.

(c) Graph the function K(x) and compare it with the graph of ƒ(x). For example, do the extrema of ƒ and K occur at the
same critical numbers? Explain your reasoning.