# Functional Grpahs and optimization

• Apr 18th 2008, 09:09 PM
someone21
Functional Grpahs and optimization
1.Locate the points on the curve y=x^2 that are closest to the point (0,4.5)?

2.A rectangle is inscribed in a circle of radius 5m.Determine the maximum possible area for such a rectangle?

The distance d from a point (x,y) to the point (0,4.5) is given by $d^2 = (x-0)^2 + (y-4.5)^2$. If the point (x,y) lies on the curve y=x^2 then we can replace x^2 by y, which gives $d^2 = y + (y-4.5)^2$. Multiply out, complete the square, and you'll find the value of y that minimises d^2.