Questions: lim as x approaches a of f(x) does not exist. Suppose a product's revenue function is given by R(q) = -3q^2 + 400q, where R(q) is in dollars and q represents the quantity of units sold. What is the marginal revenue when 50 units are sold? 12500 100 50 -100 Consider the function f(x) = ln(x^2 + 4x + 12). To compute f'(x), we use

lim as x approaches a of f(x) does not exist.

Suppose a product's revenue function is given by R(q) = -3q^2 + 400q, where R(q) is in dollars and q represents the quantity of units sold. What is the marginal revenue when 50 units are sold?

12500
100
50
-100

Consider the function f(x) = ln(x^2 + 4x + 12). To compute f'(x), we use

Transcript text: \[ \lim _{x \rightarrow a} f(x) \text { DNE. } \] Question 3 1 pts Suppose a product's revenue function is given by $R(q)=-3 q^{2}+400 q$, where $R(q)$ is in dollars and $q$ represents the quantity of units sold. What is the marginal revenue when 50 units are sold? Hint: The marginal revenue is the derivative of the revenue. 12500 100 50 $-100$ Question 4 1 pts Consider the function $f(x)=\ln \left(x^{2}+4 x+12\right)$. To compute $f^{\prime}(x)$, we use Search

Solution

Solution Steps

Solution Approach

To find the marginal revenue when 50 units are sold, we need to compute the derivative of the revenue function $ R(q) $ with respect to $ q $. This derivative, $ R'(q) $, represents the marginal revenue. After finding the derivative, we evaluate it at $ q = 50 $.

Step 1: Define the Revenue Function

The revenue function is given by: \[ R(q) = -3q^2 + 400q \]

Step 2: Compute the Derivative

To find the marginal revenue, we need to compute the derivative of $ R(q) $ with respect to $ q $: \[ R'(q) = \frac{d}{dq}(-3q^2 + 400q) = -6q + 400 \]

Step 3: Evaluate the Derivative at $ q = 50 $

Substitute $ q = 50 $ into the derivative to find the marginal revenue when 50 units are sold: \[ R'(50) = -6(50) + 400 = -300 + 400 = 100 \]