Question

section 2.12: implicit differentiation and related rates (homework)
score: 30/90 answered: 3/9
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question 4
0/10 pts 4 99 details
a companys revenue from selling x units of an item is given as ( r = 1300x - 3x^{2} ). if sales are increasing at the rate of 30 units per day, how rapidly is revenue increasing (in dollars per day) when 140 units have been sold?
dollars per day
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Explanation:

Step1: Differentiate revenue function

Differentiate \( R = 1300x - 3x^{2} \) with respect to time \( t \) using the chain rule.
\(\frac{dR}{dt}=(1300 - 6x)\frac{dx}{dt}\)

Step2: Substitute values

Given \( x = 140 \) and \(\frac{dx}{dt}=30\).
Substitute into \(\frac{dR}{dt}=(1300 - 6x)\frac{dx}{dt}\):
\(\frac{dR}{dt}=(1300-6\times140)\times30\)
First calculate \(1300 - 6\times140=1300 - 840 = 460\)
Then \(460\times30 = 13800\)

Answer:

\(13800\)