2 Answers
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C = 0.001x³ + 4x + 1024
unit cost f(x) = C/x = 0.001x² + 4 + 1024/x
f'(x) = 0.002x - 1024/x²
Set first derivative to zero
0.002x - 1024/x² = 0
0.002x = 1024/x²
0.002x³ = 1024
x³ = 512·10³
x = ∛512·10 = 80
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average cost per unit A(x) = C(x)/x = 0.001x^2 + 4 + (1024/x)
dA/dx=0
solve for x