The cost, in dollars, of producing x yards of a certain fabric is given by C(x) = 84 + 0.16x – 0.0006x2 + 0.000003x. 1. Find the average rate of change of C over the interval [80, 120]. What does this value represent in the context of this problem? Include correct units. 2. Find C'(100). What does this value represent in the context of this problem? Include correct units.

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A: To find the equilibrium point we have to put  D(x)= S(x) and solve for x .

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A: We can solve as follows

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A: answer is in next step

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A: The objective of the question is determine the 10th order derivative.

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A: To evaluate the integral.

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A: Find your answer below

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A: Since tha value of both the limit is different  Hence the limit does not exist.

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A: Explanation of the answer is as follows

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A: Region is bounded by the given curve y=e2x , y=e7x  and  x=1

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A: This question can be solved using the concept of methods of approximation of roots.

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Q: %3D

A: Solving

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A: We can find the 1st, 2nd and 3rd derivative as below.

Q: The cost, in dollars, of producing x yards of a certain fabric is given by C(x) = 84 + 0.16x –…

A: Topic:- application of derivatives

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A: Given query is to find the integral.

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A: We have to find the integral using left and right endpoints.

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A: Let's find.

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A: Use power series for finding  solution.

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A: Explanation of the answer is as follows