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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 interpretyour answer.

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00:35

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Campbell University

Oregon State University

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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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

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Harvey Mudd College

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