急 ! F6數1題 #17.

a)
f(x) = -x² + 36x
=-(x²-36+324) +324
=-(x-18)²+324

vertex is (18,324)

b)
Let the width of the rectangle be y
3x+2y=108
A=xy
=(x)(108-3x)/2
=(1/2)(-3x²+108x)
=(3/2)(-x²+36)
using a) above
=(3/2)[f(x)]

A(max) = (3/2)(324)
=486 < 500

2014-02-22 13:16:39 補充：
打錯！

A=xy
=(x)(108-3x)/2
=(1/2)(-3x²+108x)
=(3/2)(-x²+ [ 36 x ])
using a) above
=(3/2)[f(x)]