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The total revenue in cents in selling $x$ pounds of coffee is given by$R(x)=10 x(100-x)^{1 / 2} \cdot$ Using differentials, determine(a) the change in the revenue as $x$ changes from 36 lbs to 36.1 lbs;(b) the percent change in the revenue as $x$ changes from 36 lbs to 36.1 lbs.

(a) 5.75(b) $0.1997 \%$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 6

Linearization and Differentials

Derivatives

Missouri State University

Oregon State University

Harvey Mudd College

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

05:03

The revenue $R$ for a comp…

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Find the rates of change o…

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For the following exercise…

03:29

Business and Economics…

in this problem were given the revenue of a company selling uh son in the amount of units. As The function R. is equal to 900 X minus 0.10.1 X. To the second power. And we're told to use the friend show to approximate the change in revenue. Its sales increased from 300 from access equal to 300 to access equal to one 3100 units. The first step is to figure out what the X. Is. So the change themselves. So we know that the X. Is equal to. That's a fact is equal to dX. Which is equal to the change itself. Unit which is 3100 minus 3000 that becomes 100. So we know that to change themselves and that's a change in the unit and unit. So um so now we can find our the R. D. S. We know our is equal to 500 ah minus zero point one X. Great. The er the become, you know the river live of uh 9 900 X. It's 900 derivative of negative 0.1 X. Squared becomes. According to the power rule. We have the two mark. The two. Yeah Maybe the 0.1 that gives you negative. Is there a point to? Ah So that becomes a the yeah so they are um nine years on this zero point two. Yeah. Now we could plug in the values for X. And Dx. We know that the R. Becomes my 100 minus zero point to uh 3000 Times of DX which is 100. We have the R. Is equal to 30,000. So what this in fares two is basically we have an increase themselves. The amount of changing our revenue become $30,000.

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