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The cost of producing $ x $ ounces of gold from a new gold mine is $ C = f(x) $ dollars. (a) What is the meaning of the derivative $ f'(x) $? What are its units?(b) What does the statement $ f'(800) = 17 $ mean?(c) Do you think the values of $ f'(x) $ will increase or decrease in the short term? What about the long term? Explain.

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02:58

Daniel Jaimes

01:15

Carson Merrill

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Campbell University

Oregon State University

Harvey Mudd College

Baylor University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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The cost of producing $ x …

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The cost of producing $x$ …

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Table 2.8 shows world gold…

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Price of Silver The figure…

Okay. First it's important to note that X. Is in ounces and F. Is in dollars. So if you're fine, if you're finding f prime years finding the derivative of F. With respect to X. That means what you're finding is the number of dollars per ounce, Okay, cost of mining gold per ounce. Okay. So not not the cost per hour or the cost per day. It's not a time thing but it cost per ounce. Okay so what does f. Prime 800 equals 17 mean well 800 oz. And so it would say uh to mine 800 ounces will cost yeah, $17 per ounce. Do you think the value of F. Prime of X will increase or decrease in the short term? What about the long term? Okay. So at first it's going to increase. Okay. The cost per ounce when you first start. Because you got to you know you got to get all the dirt out of the way and I don't know, I don't know what lines are like but at first it's going to increase and then it'll get to a place where you know you just go in and they're like oh there's a gold, I'll take it and then the the cost will decrease in the long term, explain because it's harder when you first start to get into the mind. All right. I hope that helps. If not just post your question again.

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