Finding point closest to origin
I have finished this problem but I'm not quite sure if this has 2 answers or 1. Here is the question.
Find the points on the parabola y= 9/2 - x^2 that are closest to the origin.
Steps I did:
Use the distance formula and got x^2 + (9/2 - x^2)^2
S'= 4x(x^2 - 4)
x = 0, x = +-2
Points I got: (-2, 1/2), (2, 1/2)
is there something I did wrong?(Thinking)
Re: Finding point closest to origin
For some arbitrary point on the parabola , the square of the distance from this point to the origin is:
Implicitly differentiating. we find:
Since the denominator has no real roots, our only critical values are:
and the first derivative test shows that minima occur at . Since the distance function is even, we know the two points are the same distance from the origin, so we include them both.
You did well! :)