Calculus question - About optimization

<p>I can't figure this question out for the life of me. I can't figure out what the primary equation is at all! He literally gave us no notes on this example.</p>

<p>Here's the question:
"Find the point on the graph of y = x^2 +1 that is closest to the point (3,1)."</p>

<p>I have no idea how to solve this.</p>

<p>Wow, subforum selection fail. Seriously, this is not the place for this question.</p>

<p>Being that as it may, if I ask you which of the following two points is closer to the origin, what would your answer be?</p>

<p>(0, 3) and (1, 1).</p>

<p>How did you do that? That’s the same way you do your problem, but you should only consider points on the curve… and instead of saying closest to the origin, do (3, 1).</p>

<p>And what points are on the curve?</p>

<p>Use the distance formula to find the distance between an arbitrary point on the curve and the selected point. Derive. You’ll find that a critical number of the derivative is what you’re looking for.</p>

<p>you have to find the distance between any point (x, y) on the curve and (3, 1) using distance formula. Find the derivative of this and equate it to 0. Use the second derivative test to determine if the critical point gives f’(x) = 0 and f’'(x) > 0. then this is ur point</p>