Question

What is the difference between the actual increase in profit as production increases from 5 to 6 units, and the marginal profit at a production level of 5 units where the profit function is given by
p(x)= 3x^2 - 5x + 2

First I plugged 5 into the equation and got 52. Then I took the derivative which is 6x -5 and plugged in 5 and got 25. 52 - 25 = 27. Is this correct?

Answer 1

No, you are not correct. But, you almost had it!

To compute the actual increase in profit, first plug in 5, then plug in 6. The difference between f(5) and f(6) is the actual.
p(x)= 3x^2 - 5x + 2
p(5) = 3(5)^2 - 5(5) + 2 = 52
p(6) = 3(6)^2 - 5(6) + 2 = 80
p(6) - p(5) = 80 - 52 = 28

To compute the marginal profit
dp/dx = 6x - 5
6(5) - 5 = 25

Actual - marginal = 28 - 25 = 3

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