Find the number of units x that produces a maximum revenue R?

Question

R=171x^2 - 0.06x^3

Looking for x=____ units

Answer 1

We can optimize R by taking the derivative of R with respect to x and setting it equal to zero. We can then solve for x and get that x = 0 or 1900. We can then use the second derivative test to determine which point is a maximum and which is a minimum. Plugging both values into the second derivative of R we get that the second derivative is positive at x = 0 and negative at x = 1900. This means R is concave up at x = 0 and concave down at x = 1900. Therefore, R is minimal at x = 0 and R is maximal at x = 1900.

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