Suppose that the daily profit (in dollars) from the production and sale of x units of a product is given by: P = 180x - (/1000) x2 - 2000 At what rate per day is the profit changing (dP/dt) when the number of units produced and sold is 100 and is increasing at a rate of 10 units per day?

Q: Suppose the cost function of a product is given as C=3q -0.0014³. If the cost is increasing at a…

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Q: Find the interest earned at 5% compounded continuously for 2 years by a continuous income stream…

A: Given the interest earned r=5%=0.05 , t=2years and PV=1250. We have to find the interest.

Q: Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Find the…

A: To find the marginal revenue we find dr/dx

Q: 3. A manufacturer determines that when x thousand units of a particular commodity are produced, the…

A: Given that: Profit function: P(x)=-400x2+6800x-12000

Q: 1. Use the Difference Quotient to find the instantaneous rate of change of 2. f(x) = -5x2 - x at x…

A: We have to find the instantaneous rate of change using difference quotient we have  f(x)=-5x2-xat…

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

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Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: The given function of production cost is To find average rate of change of total cost ,use formula

Q: Find the present value of a continuous stream of income over 3 years if the rate of income is…

A: Given the rate of income , ft=80e-0.08t Number of yearsT=3 Interest rater=11% The present value can…

Q: You have a large metal box filled with honey, where the width is 14 cm, the length is half its size,…

A: For the metal box, it is given that width is b=14 cm, Length is half of width, l=7 cm,  Volume is…

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.9x2 −…

A: To calculate the marginal revenue by differentiating the revenue function.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.8x2 -…

A: The revenue (in dollars) from the sale of a product is given by, R=60x+0.8x2-0.003x3, where x is the…

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: Given that a company can produce 12,000 units when the number of hours of skilled labor y and…

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

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Q: Suppose the amount of oil pumped from one ofthe canyon wells in Whittier, California, decreases at…

A: We know that general exponential function is  y=y0e-kt California, decreases at the continuous rate…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by…

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Q: 4) Determine the instantaneous rate of change at x = 2 for f(x) = 2x2 + 4x

A: We have to find instantaneous rate of change

Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: Find the PV of an income stream paying out continuously at a rate of     5000e−0.1t dollars per year…

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Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Suppose total cost in dollar from the production of x printers is given byC(x) =…

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A:

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: Given query is to find the rate of change of cost.

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: From the given data:

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

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Q: If total revenue is R=50Q-2Q^2. At what value of Q will marginal revenue by -10?

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Q: Suppose the amount of oil pumped from one of canyon near the beach of island decreases at the…

A: Given query is to find the time when output will become one fifth of initial value.

Q: If the total revenue function for a blender is R(x) = 28x – 0.01x² where x is the number of units…

A: To find The average rate of change of revenue R(x) as x increases from 10 to 20 units.

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.8x2 −…

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Q: Suppose that value of wine respect to time is given following function V = 100e ve. How long will it…

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 20x + 0.5x² -…

A: Given: Revenue function from the sale of a product is given by: ⇒R=20x+0.5x2-0.002x3

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

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A: We need to find rate.

Q: Suppose that the amount of water pumped from a water well decreases at a continuous rate of 10% per…

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Q: Suppose that the marginal revenue for a company manufacturing coffee machines is given by 100−0.5x…

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Q: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

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Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

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Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

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Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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Q: Suppose to tal cost indollars from the production of X printers is given by C/X=.000xt o005x²+28X+…

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Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: