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A company's revenue from selling x units of an item is given as R=1700x-2x^2 . If sales are increasing at the rate of 25 units per day, how rapidly is revenue increasing ( in dollars per day ) when 250 units have been sold

Respuesta :

MrRoyal

Answer:

The daily rate is: 17500 units per day

Step-by-step explanation:

Given

[tex]R = 1700x - 2x^2[/tex]

[tex]\frac{dx}{dt} = 25[/tex]

Required

Find [tex]\frac{dR}{dt}[/tex] when [tex]x = 250[/tex]

We have:

[tex]R = 1700x - 2x^2[/tex]

Differentiate both sides with respect to time

[tex]\frac{dR}{dt} = 1700\frac{dx}{dt} - 4x\frac{dx}{dt}[/tex]

Factorize

[tex]\frac{dR}{dt} = (1700- 4x)\frac{dx}{dt}[/tex]

Substitute: [tex]\frac{dx}{dt} = 25[/tex] and [tex]x = 250[/tex]

[tex]\frac{dR}{dt} = (1700- 4x)\frac{dx}{dt}[/tex]

[tex]\frac{dR}{dt} = (1700- 4*250)*25[/tex]

[tex]\frac{dR}{dt} = (1700- 1000)*25[/tex]

[tex]\frac{dR}{dt} = 700*25[/tex]

[tex]\frac{dR}{dt} = 17500[/tex]

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