Differentation 的问题

JiaHuan1995

Find two nonnegative numbers x and y whose sum is 300 and which x^2y is a maximum.

which x^2y is a maximum. (这一句是什么意思?)

可以帮我solve这一题吗？谢谢！

JiaHuan1995

还有一题。

An inverted right circular cone has a semi-vertical angle of 30'. Water runs out of a small hole at the vertex of the cone at a constant rate of 3cm^3/s. Find the rate at which the depth h of the water is falling when the volume of water is 81 (pi) cm^3.

menglee

1. x^2y is a maximum代表differentiate过后会等于零。用x和y的关系就可以做到：x+y=300。

2. 用trigonometry找出radius和height的关系，如果是30degree代表cos 30=r/h，那么h等于r/cos30。再把h带入cone的formula, V=pi*r^2*h。Differentiate过后用chain rule: dV/dt=dv/dh*dh/dt。

以上是一个form 5生能做到的而已，有请版主赐教。

JiaHuan1995

x^2y is a maximum代表differentiate过后会等于零？

dy/dx , 2xy + x^2dy/dx  = 0 ?
so,  dy/dx = -2y/x ?

很blur咧，不是很明白。

flash

x + y = 300
y = 300 - x ---(1)
假设 t = x^2y = x^2(300 - x)
dt/dx = 600x - 3x^2
d^2t/dx^2 = 600 - 6x
所以 x 是 200.
如此从 (1) 可算出 y 是 100.