please help me with algebra 2

Question

The weight of an ideal cut round diamond can be modeled by f(d)=o.0071d^3-0.090d^2+0.48d

where d is the diameter of the diamond. find the domain of the function in context of the situation

possible answers

A) the domain is all real numbers

B) the domain is {d|d>0}

c) the domain is {d|d<0}

D) the domain is {d|d>0.48}

Answer 1

We need 0 < 0.0071d³ – 0.090d² + 0.48d = (0.0071d² – 0.090d + 0.48)d = 0.0071(d² – (900/71)d + 4800/71)d = 0.0071((d – 450/71)² + 138300/5041)d which is always the case if d > 0.