A cost function is given for a certain commodity. Find the marginal cost function. Then compare the marginal cost at the production level of 100 units with the cost of producing the 101st item.

jCCCCCCCCC(x) = 420 + 1.5x + 0.002x2

Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm3/s. How fast is the radius of the balloon increasing when the diameter is 50 cm?

Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.3 mi and car B is 0.4 mi from the intersection?

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Dialectical Notes