Question

the revenue of this product is given by R=px=(100x-x^2)x. how many units must be sold to give zero revenue? p=100x-x^2

Answer 1

R(x) is the revenue as a function of the number of units sold, x, where

R(x)=(100x-x²)x

if p(x)=100x-x² then R(x)=0 whenever p=0.

So the problem would be reduced to solve for p(x)=0, or
100x-x²=0
x(100-x)=0
which gives us x=100 would make p(x)=0 and R(x)=0.

Put x=100 back into R(x) to make sure the answer is correct.