Monotony, Concave Up/Concave Down problem

Oct 2007
121
1
France
f(x)=sqrt(u(x)), where u(x)=x^3/(x-2)
The function f is defined for x>2 or x<=0

f '(x)=u '/(2sqrt(u))

u '(x)=2x²(x-3)/(x-2)²
The function f ' is defined for x>2 or x<0.

f '(x)=0 if x=3
f '(x)>0 for x>3 and f '(x)<0 for x<3
 
Nov 2007
13
0
Richard André-Jeannin said:
f(x)=sqrt(u(x)), where u(x)=x^3/(x-2)
The function f is defined for x>2 or x<=0

f '(x)=u '/(2sqrt(u))

u '(x)=2x²(x-3)/(x-2)²
The function f ' is defined for x>2 or x<0.

f '(x)=0 if x=3
f '(x)>0 for x>3 and f '(x)<0 for x<3
thanks...I see I can solve it this way!
but still wondering why tabular way isn't working...(where's my mistake?)