marginal values
Find the function that describes the marginal revenue for

Ask by Owen Robbins. in the United States

Dec 07,2024

Question

marginal values Find the function that describes the marginal revenue for $$ R=30 x^{2 / 2 / 3}-2 x $$

UpStudy AI · Accepted Answer

To find the marginal revenue, we need to compute the derivative of the revenue function $$ R $$ with respect to $$ x $$. The given revenue function is:

$$
R = 30x^{2/3} - 2x
$$

Now, let's differentiate $$ R $$ with respect to $$ x $$:

1. Differentiate $$ 30x^{2/3} $$:
   $$
   \frac{d}{dx}(30x^{2/3}) = 30 \cdot \frac{2}{3} x^{(2/3) - 1} = 20x^{-1/3}
   $$

2. Differentiate $$ -2x $$:
   $$
   \frac{d}{dx}(-2x) = -2
   $$

Now, combine these results to find the marginal revenue $$ R' $$:

$$
R' = 20x^{-1/3} - 2
$$

Thus, the function that describes the marginal revenue is:

$$
R' = 20x^{-1/3} - 2
$$

This can also be expressed as:

$$
R' = \frac{20}{x^{1/3}} - 2
$$

This is the marginal revenue function.
The marginal revenue function is $$ R' = 20x^{-1/3} - 2 $$ or $$ R' = \frac{20}{x^{1/3}} - 2 $$.

marginal values
Find the function that describes the marginal revenue for

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