Consider the function f(x)=x²+c
Let P=(x,y) be a point on the graph of y=x²+c
Let d(x) = the distance from P to the origin.

[1] Find the value(s) of x, in terms of c, that minimizes d(x).

[2] Prove d(x) ≥ f(x) for all x and c.

[3] Find, in terms of c, the limit as x goes to infinity of d(x)-f(x)

[4] Find, in terms of c, and if it exists, the integral from negative infinity to positive infinity of (d(x)-f(x)-the above limit) dx

I accidentally made my solution public, but it does not contain part 4.  I never managed to find the solution.

Posted by Jer on 2012-10-05 10:57:06