Question: Please show work. Problem 8: A spherical balloon is being inflated, Find the rate of increase of the surface area of the balloon (S =

Please show work.

Problem 8: A spherical balloon is being inflated, Find the rate of increase of the surface area of the balloon (S = 472) with respect to the radius r. Then give the rate of change when r is 1 foot, 2 feet, and 3 feet. What conclusion can you make about the balloon? Problem 9: The cost, in dollars, of producing a yards of a certain fabric is C(x) = 12000 + 12x - 0.1x2 + 0.000523 Find the marginal cost function. Then find C'(200) and explain its meaning and what it might predict. Finally compare C'(200) with the cost of manufacturing the 201st yard of frabric

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