The following function gives the cost, in dollars, of producing x kilograms of fertilizer: C(x) = 0.001x^3...

Question

The following function gives the cost, in dollars, of producing x kilograms of fertilizer:
C(x) = 0.001x^3 - 0.14x^2 + 7x + 160
What is the instantaneous rate of change of the cost when 50 kilograms are produced?
Choose 1 answer:
A. -6.5 kilograms per dollar
B. -6.5 dollars per kilogram
C. 0.5 kilograms per dollar
D. 0.5 dollars per kilogram

SnapAndSolve AI · Accepted Answer

To find the instantaneous rate of change of the cost, we need to find the derivative of the cost function C(x) and evaluate it at x = 50.

The derivative C'(x) is:

C'(x) = 0.003x^2 - 0.28x + 7

Now, evaluate C'(x) at x = 50:

C'(50) = 0.003(50)^2 - 0.28(50) + 7
= 0.003(2500) - 14 + 7
= 7.5 - 14 + 7
= 0.5

The instantaneous rate of change of the cost when 50 kilograms are produced is 0.5 dollars per kilogram.

Answer: D. 0.5 dollars per kilogram

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The following function gives the cost, in dollars, of producing x kilograms of fertilizer: C(x) = 0.001x^3...

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