Problem

The Michaelis-Menten equation for the enzyme chym…

03:51

Problem 58 Medium Difficulty

A manufacturer produces bolts of a 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) $.

(a) What does it mean to say that $ f (20) = 10,000 $ and $ f'(20) = - 350? $
(b) Assuming the values in part (a), find $ R'(20) $ and interpret
your answer.

Answer

(a) See explanation
(b) $R^{\prime}(20)=3000$

More Answers

00:35

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

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Video Transcript

he excludes the one you radio. So for part A, we have two interpretations. The 1st 1 which is up 20 equals 10,000 says that if the price is $20 in 10,000 units will be sold for the derivative of 20 equals Negative. 3 50 means that increasing the selling price by $1 will decrease sails by 350 units. For Part B. We're going to do a calculation. So first we're going to have our of P equal. P times are 50. We differentiate our we get P terms, the derivative of of P less one times of p. We plug in 20 when we get the derivative of 20 equal to 20 times negative 3 50 plus one terms, 10,000 just equal to 300 3000 excusable. And since it's positive means that increasing the selling price will increase the revenue

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College