A manufacturer produces bolts of fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write
q = f(p).
Then the total revenue earned with selling price p is
R(p) = pf(p).
Given
f(15) = 7000
and
f '(15) = −330,
find
R'(15).

Question

A manufacturer produces bolts of fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write 
q = f(p).
 Then the total revenue earned with selling price p is 
R(p) = pf(p).
 Given 
f(15) = 7000
 and 
f '(15) = −330,
 find 
R'(15).

anonymous · Answer

R'(p) = p f'(p) + f(p) 
R'(15) = 15 ( -330 ) + 7000
          = -4950+ 7000
           = 2050