section 2.12: implicit differentiation and related rates (homework)\nscore: 30/90 answered: 3/9\nprogress…

section 2.12: implicit differentiation and related rates (homework)\nscore: 30/90 answered: 3/9\nprogress saved done \nquestion 4\n0/10 pts 4 99 details\na 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?\ndollars per day\nquestion help: video\nsubmit

section 2.12: implicit differentiation and related rates (homework)\nscore: 30/90 answered: 3/9\nprogress saved done \nquestion 4\n0/10 pts 4 99 details\na 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?\ndollars per day\nquestion help: video\nsubmit

Answer

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)