Question

A monopolist demand curve is p=100-2q a) find marginal revenue function b) at what price is marginal revenue is zero

Answer 1

Demand curve =  p  = 100 - 2 q
   q = quantity        and  p = demand
  
R (q) = Revenue = demand * quantity = p q = 100 q - 2 q²

Revenue from a demand or selling of q-1  items = R(q-1)
     = 100 (q-1) - 2 (q-1)² = 100 q - 100 - 2 q² + 4 q - 2

Marginal revenue function =  R(q) - R(q-1) = 102 - 4 q

MR = 0  =>  102 = 4 q  =>    q = 25.5  ie.,  25 or 26.  we can take..
   Marginal revenue is not exacty zero.  Its a small loss (-2) when q = 25  and very small (+2) when q = 26.

===========================

R(q) = 100 q  - 2 q²
 if we use calculus to differentiate the revenue:
             MR(q) = marginal revenue:  100 - 4 q
     MR(q) = 0  for  q = 25.