I need help with this problem:
the first thing to do is to convert the above question to a root finding problem.
you can do so by first finding distance of an arbituary point on the curve from (-3,0).
you should get the equation of d = sqroot( (Xo - (-3) )^2 + (f(Xo) - 0 )^2 ) , where (Xo, f(Xo)) is an arbituary point on the curve.
since distance in this case has an absolute minimum, use Newton's Method to find the root of this derivative, d'(Xo) = 0, to solve for the value of Xo where this absolute minimum occurs, ie, the point closest to (-3, 0).
Hope this helps!
Differentiating and equating to zero
leading to a cubic
Using Newton's method
Finally, choose an initial estimate for x and run through a few iterations
to find the x co-ordinate of the point of contact of the tangential circle.