Question

If the cost of producing $x$ items is given by the function $C(x),$ and the total revenue when $x$ items are sold is $R(x),$ then the profit function is $P(x)=R(x)-C(x) .$ Show that the instantaneous rate of change in profit is 0 when the marginal revenue equals the marginal cost.

Name: If the cost of producing x items is given by the function C(x), and the total revenue when x items are sold is R(x), then the profit function is P(x)=R(x)-C(x) . Show that the instantaneous rate of change in profit is 0 when the marginal revenue equals the marginal cost.
Uploaded: 2022-11-23T08:54:36-08:00
Duration: 3 min
Channel: Sri K
Description: If the cost of producing x items is given by the function C(x), and the total revenue when x items are sold is R(x), then the profit function is P(x)=R(x)-C(x) . Show that the instantaneous rate of change in profit is 0 when the marginal revenue equals the marginal cost.

          If the cost of producing $x$ items is given by the function $C(x),$ and the total revenue when $x$ items are sold is $R(x),$ then the profit function is $P(x)=R(x)-C(x) .$ Show that the instantaneous rate of change in profit is 0 when the marginal revenue equals the marginal cost.

Added by Cody S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

11/23/2022

Step 1

The instantaneous rate of change in profit is given by the derivative of the profit function, which is $P'(x)=R'(x)-C'(x)$. The marginal revenue is the derivative of the revenue function, $R'(x)$, and the marginal cost is the derivative of the cost function, Show more…

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If the cost of producing $x$ items is given by the function $C(x),$ and the total revenue when $x$ items are sold is $R(x),$ then the profit function is $P(x)=R(x)-C(x) .$ Show that the instantaneous rate of change in profit is 0 when the marginal revenue equals the marginal cost.