Problems with absolute maximum and minumum word problem.?

Question

I can't seem to get anything logical out of this through deriving it.

F= (uW)/(usin(Theta) + cos(Theta))
where u is a positive constant, W is objects weight (irrelevant) and where 0 <= Theta <= pi/2. Show that F is minimized when tan(Theta) = u.

Answer 1

F= (uW)/(usinθ + cosθ)
dF/dθ = -uW(ucosθ - sinθ)/(usinθ + cosθ)^2
when dF/dθ = 0, the fuction is a minimum or maximum:
-uW(ucosθ - sinθ)/(usinθ + cosθ)^2 = 0
-uW(ucosθ - sinθ) = 0
ucosθ - sinθ = 0
ucosθ = sinθ
u = sinθ/cosθ
u = tanθ

Answer 2

If your still confused after reading the previous answer which is quit right then try making the derivitive equal to zero and you can find the derivitive by using the following two rules:
1) quotient rule: Derivitive of one fuction devided by another is equal to (the derivitive of the numerator times the denominator) minus (the numerator times the derivitive of the denominator) all over the square of the denominator.
eg: Derivitive of 8x/4x= (4x*8)-(8x*4)/16(x^2)=64x/16(x^2)=4/x

2) The product rule: the derivitive of (a) multiplied by (b) is equal to (a) times the derivitive of (b) plus (b) times the derivitive of (a). (note derivitive of u=0 as it is a constant.)

Also note:
derivitive of sinx=cosx
derivitive of cosx= negative sinx