Thread: 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?

Please provide full steps!

Originally Posted by someone21

1.Locate the points on the curve y=x^2 that are closest to the point (0,4.5)?

We want to minimise a distance, but in practice it's easier to minimise the square of the distance.

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