數學 about dy/dx (20)

a. y=(x^2 + 9)/2x
dy/dx=[(2x)(2x)-(x^2+9)(2)]/(2x)^2
=(2x^2-18)/4x
=(x^2-9)/2x

b. put dy/dx=0
0=x^2-9
x=3 or -3

x<-3, dy/dx<0
x=-3, dy/dx=0
-3<x<3, dy/dx>0
x=3, dy/dx=0
x>3, dy/dx<0

min. x is -3
max. x is 3

min values of y is -3
max values of y is 3

2009-12-13 23:27:12 補充：
睇唔到果部份係

x<-3, dy/dx<0
x=-3, dy/dx=0
-3<3, dy/dx>0
x=3, dy/dx=0
x>3, dy/dx<0

2009-12-14 00:25:44 補充：
amaths書微分果課應該有講到呢個formular,,

條formular係

y=ax+c/bx

dy/dx= {[d(ax+c)/dx]bx-(ax+c)[d(bx)/dx]} / (bx)^2

a. y=(x^2 + 9)/2x
dy/dx=[(2x)(2x)-(x^2+9)(2)]/(2x)^2
=(2x^2-18)/4x
=(x^2-9)/2x

b. put dy/dx=0
0=x^2-9
x=3 or -3

x&amp;lt;-3, dy/dx&amp;lt;0
x=-3, dy/dx=0
-3&amp;lt;x&amp;lt;3, dy/dx&amp;gt;0
x=3, dy/dx=0
x&amp;gt;3, dy/dx&amp;lt;0

min. x is -3
max. x is 3

min values of y is -3
max values of y is 3 2009-12-13 23:27:12 補充



x&lt;-3, dy/dx&lt;0
x=-3, dy/dx=0
-3&lt;3, dy/dx&gt;0
x=3, dy/dx=0
x&gt;3, dy/dx&lt;0



amaths formular,,

formular係

y=ax+c/bx

dy/dx= {[d(ax+c)/dx]bx-(ax+c)[d(bx)/dx]} / (bx)^2