Find minimal average cost calculus

I will give best answer to anyone who can help
C(x) = 250 [sqrt[x]] + x^2 /42875
A) Find the minimal average cost

Average cost = cost / number of units

so take c(x) and divide by x, we get 250 x^1/2/x + x^2/42875x= 250x^(-1/2) + x/42875
now to get the minimum, take derivative and set it equal to 0.

-125x^(-3/2)+1/42875=0
-125/x^(3/2)=-1/42875
x^(-3/2)= 1/(42875*125)
x^(3/2)= 42875*125= 5359375
x^1/2= 175
x= 30625