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6. Suppose that the cost (in dollars) for a company to produce \(x\) pairs of a new line of jeans is \(C(x) = 5000 + 3x + 0.01x^2 + 0.0002x^3\) (a) Find the average rate of change of cost from \(x = 100\) to \(x = 200\). (b) Find the marginal cost function. (c) Find the marginal cost for \(x = 100\). (What does this mean?) (d) Find the linear approximation for the cost function at \(x = 100\). Hint: use the equation of the tangent line at \(x = 100\). (e) Use the linear cost function from part (d) to find the cost of manufacturing 101 pair of jeans.

          6. Suppose that the cost (in dollars) for a company to produce \(x\) pairs of a new line of jeans is
\(C(x) = 5000 + 3x + 0.01x^2 + 0.0002x^3\)
(a) Find the average rate of change of cost from \(x = 100\) to \(x = 200\).
(b) Find the marginal cost function.
(c) Find the marginal cost for \(x = 100\). (What does this mean?)
(d) Find the linear approximation for the cost function at \(x = 100\). Hint: use the equation of the tangent line at \(x = 100\).
(e) Use the linear cost function from part (d) to find the cost of manufacturing 101 pair of jeans.

6. Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is
C(x) = 5000 + 3x + 0.01x^2 + 0.0002x^3
(a) Find the average rate of change of cost from x = 100 to x = 200.
(b) Find the marginal cost function.
(c) Find the marginal cost for x = 100. (What does this mean?)
(d) Find the linear approximation for the cost function at x = 100. Hint: use the equation of the tangent line at x = 100.
(e) Use the linear cost function from part (d) to find the cost of manufacturing 101 pair of jeans.

Added by Vanesa A.

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