The product of two positive numbers is 675 minimize the sum of the first and three times the second

Hello : 
xy = 675...(1)
x >0 and y >0
by (1) : y = 675/x
x+3y =  x+3(675)/x = x +2025/x
let : f(x) = x +2025/x
calchlate the minumum:
f'(x) = 1- 2025/x²
f'(x) = (x²-2025)/x²
f'(x) = 0   : x²-2025 =0
x² =2025 =45²
x = 45 ( x >0 )
sign of f'(x) : -∞ـــــــــــــــــــــــــــــــــــــــــ   45ــــــــــــ/0/ـــــــــــ  45 -ـــــــــــــــــــ>+ ∞ 
                        0   0
f(45) is a minumum value
f(45) = 90 (  minimize the sum of the first and three times the second)    

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