08- CE A.MATHS SQ 第13題

Not difficult

(a)

y=x(x-6)^2=x(x^2-12x+36)=x^3-12x^2+36x

dy/dx=3x^2-24x+36

d^2y/dx^2=6x-24

Let dy/dx=0

3x^2-24x+36=0

x^2-8x+12=0

(x-2)(x-6)=0

x=2 or 6

when x=2 , d^2y/dx^2=6x-24=-12＜0

when x=6 , d^2y/dx^2=6x-24=12＞0

So (2,32) is a maximum point

(6,0) is a minimum point

(b)

Notice that

when x<2 dy/dx＞0

when 2＜x＜6 dy/dx＜0

when x＞6 dy/dx ＞0

Using this information, you can draw the graph easily

There is a graph calculator which can sketch the graph

http://webgraphing.com/graphing_basic.jsp

2008-05-18 17:34:08 補充：
最重要條graph要過(0,0)

而且因為那三個區域都是單調遞增或遞減﹐所以好易畫