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 $P ( x ) = 3 x ^ { 2 } - 5 x + 2 ?$
A) 25
B) 3
C) 27
D) 0
E) 6

Question

Quizplus · Accepted Answer

The actual increase in profit as production increases from 5 to 6 units is calculated by finding the difference in profit at these two production levels using the given profit function $P(x) = 3x^2 - 5x + 2$. For $x = 5$, $P(5) = 3(5)^2 - 5(5) + 2 = 75 - 25 + 2 = 52$. For $x = 6$, $P(6) = 3(6)^2 - 5(6) + 2 = 108 - 30 + 2 = 80$. The actual increase in profit is $80 - 52 = 28$.The marginal profit at a production level of 5 units is the derivative of the profit function evaluated at $x = 5$. The derivative of $P(x) = 3x^2 - 5x + 2$ is $P'(x) = 6x - 5$. Evaluating this at $x = 5$ gives $P'(5) = 6(5) - 5 = 30 - 5 = 25$.The difference between the actual increase in profit and the marginal profit at a production level of 5 units is $28 - 25 = 3$.

What Is the Difference Between the Actual Increase in Profit P(x)=3x2−5x+2?P ( x ) = 3 x ^ { 2 } - 5 x + 2 ?P(x)=3x2−5x+2?

What Is the Difference Between the Actual Increase in Profit $P ( x ) = 3 x ^ { 2 } - 5 x + 2 ?$