The net profit in dollars per day for a small business owner is given by the equation f (x) = -0.1x² + 8x + 1, where x is the number of employees he hires. If he hires the number of employees that will maximize his profit, what will his profit be in dollars per day? (Enter an exact number.)

Q: Show that the equation f(x) =x+3x-1%=Ø %3D has at least one solution,

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Q: Approximate the value of the root of f(x)=-3x³+5x²+14x-16 near x=3 to within 0.05 of its actual…

A: Given : f(x)=-3x3+5x2+14x-16, to find the value of the root near x=3.

Q: For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue…

A: Given: Revenue cost: R(x)=-0.5 x-902+4050;   Cost function:…

Q: The annual revenue and cost functions for a manufacturer of grandfather clocks are approximately…

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Q: A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x…

A: We first find the profit function.  P(x)=R(x)-C(x)P(x)=px-C(x)P(x)=(5 − 0.0003x)x-700 + 3x +…

Q: The graph of f(x) = 2x° + 15x² – 84x + 18 has two horizontal tangents. What is the negative value of…

A: Here, f(x)=2x3+15x2-84x+18

Q: What are the coordinates at the minimum point of f(x)= x2-4x+3?

A: f(x)= x2-4x+3 is a parabola with a positive lead coefficient so it will have a minimum at the…

Q: A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x…

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Q: Find a formula for the quadratic function whose graph has y-intercept at y=11 and zeros at x=1 and…

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Q: R = 840x + 207x² – x³ X = units

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Q: Suppose we have a revenue function given by  R(x) = 3x3 - ax, Where a is a constant. What would the…

A: Average revenue=Revenuex=R(x)x

Q: If f(x)=4x2-2x+3 solve f'(x)=28

A: We first find f'(x) using exponent rule: [d/dx(x^n)= n*x^(n-1)]

Q: Find the number of units x that produces a maximum revenue R in the given equation. R = 33x2/3 – 2x…

A: Given:- R = 33x(2/3) -2x To find:- Number of units x produces a maximum revenue R

Q: How would you solve for f(x)=x2+6 g(x)=2x+3 (gof)(-2)

A: Given, f(x)=x2+6   g(x)=2x+3  We have to find g∘f-2

Q: For a certain company, the cost function for producing x items is C(x)=30x+100 and the revenue…

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Q: The graph of f(x) = 2x³ + 6x² horizontal tangents. – 90x + 8 has two What is the negative value of x…

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Q: A study of the exercise habits of 17,000 alumni from a certain college found that the death rate…

A: We are given the death rate function as R(x)=5x² − 35x + 108 where x is the weekly amount of…

Q: If Q(x) =  x^3 − 25x + 100 is the cost per item of producing x-items. Is the cost per item…

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Q: Solve ivp  f'(x) = x^3-7x^2+8x-3 ; f(0) = 3

A: Given ,  f'(x) = x3 - 7x2 + 8x - 3 ; f(0) = 3 Take , integration both sides w.r.t x Then ,  ∫ f'(x)…

Q: The weekly revenue from the production and sale of x units of grain is given by R(x) = 237x - x…

A: The weekly revenue from the production and sale of x units of grain is given by- R(x)=237x-x2 The…

Q: artwork has a cost function

A: Cost function C(x)=24x+300 Revenue function R(x)=75x Where x is the number of item made We know…

Q: For a certain company, the cost function for producing x items is c (x)=50x+150 and the revenue…

A: It is given that c(x)=50x+150 and R(x)=-0.5(x-110)2+6050.

Q: The weekly revenue from the sale of x units of a service is given by R(x) = 192x - 6x thousand…

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Q: Why does the graphy of the quadratic function f(x)=x2+4x+5 cross the y-axis but not the x-axis?

A: The graph the quadratic function crosses y axis because we can put x is equal to zero and get y…

Q: Solve for f(2) f(x)=-3x+3 f(2)=?

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Q: Find the number of units that must be produced and sold in order to yield the maximum profit given…

A: Consider the revenue and cost function

Q: Is function  y=x2 a solution for equation of (1-x3)y'-2x+x2y+y2=0? If it is, find the solution.

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Q: C(x) = 600 + 7x + 0.0002x2.  Each racket can be sold at a price of p dollars, where p is related to…

A: Since it is given that each racket can be sold at a price of p dollars and we have x number of…

Q: The net profit in dollars per day for a small business owner is given by the equation f (x) =…

A: Given function  f(x)=-0.1x^2+8x+1 where x=number of employees, f(x)=Profit function  f'(x)=-0.2x+8…

Q: The value of x which satisfy 3x + 1| < - is : 5.

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Q: A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x? - 250x…

A:

Q: A laptop company has discovered their daily cost and revenue functions:  C (x) = 3x2 − 10x + 200…

A: The cost function is, C(x)=3x2−10x+200 The revenue function is, R(x)=−2x2+100x+50

Q: The graph of f(x) = 2x + 6x2 – 90x + 21 has two horizontal tangents. What is the negative value of x…

A: Given that the graph of f(x)=2x3+6x2-90x+21-(i) has two horizontaltangents.Our Aim is to tell the…

Q: The path a diver takes from the diving platform is modeled by the equation f (x) = –,x² + 3x + 12…

A: find the maximum height

Q: Solve the initial condition problem: f"(x) = 60x³ + 24x², f(2) = 239, f(-3) = 254

A: f''x=60x3+24x2 take integration  ∫ f''x=∫ 60x3+24x2dx f'x=∫60x3dx+∫ 24x2dx f'x=60x44+24x33+C…

Q: Find the point(s) of intersection. f(x) = 2x2 − 7x − 18 and g(x) = 3x + 10

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Q: use quadratic functions. Suppose that the cost function for a particular item is given by the…

A: We have to use quadratic functions. The cost function for a particular item is given by the…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: Given relation:P(x)=50x-0.25x2Where,P(x)=Profitx-number of tickets Differentiate P(x) with respect…

Q: A business has a cost function C(x) = 110x + 489.65 and a revenue function R(X)= 245 x + 32.…

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Q: what is the end function. f(x)=120+39x+3x^2

A: Given function,  f(x)=120+39x+3x^2   As it is quadratic equation, with upward opening.    Thus end…

Q: A duck dives under water and its path is described by the quadratic function y=2x-4x, where y…

A: y=2x2-4x The position of duck to dive down 2 meters y=-2 -2=2x2-4x 2x2-4x+2=0 2(x2-2x+1)=0…

Q: The daily profit from the sale of a product is given by P = 32x − 0.2x2 − 200 dollars, where x is…

A: topic - application of derivatives

Q: The weekly revenue from the production and sale of x units of salt is given by R(x)=54x−x^2 thousand…

A:

Q: The weekly revenue from the production and sale of x units of salt is given by R(x) = 172x – 2x²…

A: Given,  Revenue function: Rx = 172x-2x2   Cost function : Cx = 2x2+148x+6            Where 0≤x≤10…

Q: Find the point at which the line f(x)3 4x6 intersects the line g(x) =-4 +2

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Q: Find the point on the graph of the equation f (x) = x² – 8 that is closest to the point (0, -2)

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Q: Find the point at which the line f(x)=−5x−10 intersects the line g(x)=−4x−8.

A: We need to find a point of intersection of both the given lines.

Q: Find the number of units that must be sold to break even.

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