A manufacturer produces bolts of a fabric with a fixed width. A 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).

Find R′(40), given f(40)=8000, and f′(40)=−250. (What does this mean?)

R′(40)=

Question

A manufacturer produces bolts of a fabric with a fixed width. A 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). 

Find R′(40), given f(40)=8000, and f′(40)=−250. (What does this mean?) 

R′(40)=

pulsified333 · Answer

@mathmale

mathmale · Answer

Since R depends upon p, the derivative of R is the derivative of R with respect to p.

Can you find that?

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