Questions: Section 2.7: Find the marginal revenue function R(x)=36x-0.03x^2 R'(x)=36-0.03x

Section 2.7: Find the marginal revenue function R(x)=36x-0.03x^2 R'(x)=36-0.03x
Transcript text: Section 2.7: Find the marginal revenue funct \[ R(x)=36 x-0.03 x^{2} \] $R^{\prime}(x)=36-0.03 x$
failed

Solution

failed
failed

Solution Steps

To find the marginal revenue function, we need to take the derivative of the given revenue function \( R(x) \).

Solution Approach
  1. Identify the given revenue function \( R(x) = 36x - 0.03x^2 \).
  2. Compute the derivative of \( R(x) \) with respect to \( x \) to find the marginal revenue function \( R'(x) \).
Step 1: Identify the Revenue Function

The given revenue function is

\[ R(x) = 36x - 0.03x^2. \]

Step 2: Compute the Derivative

To find the marginal revenue function, we compute the derivative of \( R(x) \):

\[ R'(x) = \frac{d}{dx}(36x - 0.03x^2). \]

Step 3: Simplify the Derivative

Calculating the derivative yields:

\[ R'(x) = 36 - 0.06x. \]

Final Answer

The marginal revenue function is

\[ \boxed{R'(x) = 36 - 0.06x}. \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers? Record your answer in the boxes below. Be sure to use the correct place value.
failedAnswered
Question 7 A single card is drawn from a standard 52-card deck. The probability of drawing a face card. (a) 12/52 (b) 4/52 (c) 1/52 (d) 8/52 (a) (b) (c) (d) Question 8 Consider tossing a coin two times in a row.
failedAnswered
Which of the following has the lowest heat of combustion ( kJ / mol) ? Cyclopentane Methylcyclopentane Methylcyclohexane Cycloheptane Methylcycloheptane
failedAnswered
The sum of the first 12 terms of a geometric sequence with 10 as the first term and a common ratio of 0.3 is a.) 14.2857 b.) 7.0001 c.) 7.6923 d) 32.8719
failedAnswered
Here again is the histogram showing the distribution of 50 ages at death due to trauma (accidents and homicides) that were observed in a certain hospital during a week. A possible value of the median in this example is 23 45 50 33 It is impossible to answer without seeing all of the data.