Gasoline Mileage From information given in a recent busi- ness publication, we constructed the mathematical model 1 M(x) = -x? + 2r – 20, 30 < x s 65, 45 to represent the miles per gallon used by a certain car at a speed of x mph. Find the absolute maximum miles per gallon and the absolute minimum and the speeds at which they occur.

Q: (b) Find the values of a and b so that the function f(x) = x2 + ax + b has a local maximum at the…

A: I have stated the used formulas in the solution

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A: Given that: f(x)=(x-1)23-1 We can re-write it as: f(x)=(x-1)23-1. Therefore,…

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Q: I need help o n this homeowrk please help FInd the maximum profit and the number of units that must…

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Q: Find the local minimum value of f(x, y) = 4 + æ° + y° – 5xy.

A:

Q: The accompanying figure shows the flow of downtown traffic during the rush hours on a typical…

A: For (A), First, we will set up linear equations describing the traffic flow.

Q: Question Find the maximum value of the function f(x, y, z) = x +y? + z subject to the constraint x4…

A: Use Lagrange method

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A: Given query is to find the the value of x where g(x) will be maximum.

Q: A car rental agency rents 200 cars per day at a rate of $30 per day. For each $1 increase in rate, 5…

A: see below the answer

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Q: A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the…

A:

Q: Find the extreme values of f(x,y) = xy subject to the constraint x2 +y2 - 6 = 0. The extrema are…

A: We use langrange multiplier method to find extreme values

Q: you for answering this question. Please you specify each step and formula you used as soon as…

A:

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A: We can calculate the minimum value at the critical point where, fx(x,y) = 0fy(x,y) = 0 fx ,fy…

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A: The population percent will be maximum when the first derivative of function p(t) equals zero. This…

Q: 4. PATH OF A DIVER The path of a diver is given by 24 y = -r + +12 where y is the height (in feet)…

A: Solve for the maximum height

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Q: Exercise Find the absolute extremum value. 1. y = x*-8x² + 16; on [-3,1] 2. y = x3 + 7x² - 5x; on…

A: This is a application of derivative problem

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A: You need to find out the critical points then solve for maxima &amp; minima. The explanation part is…

Q: A laser rangefinder is locked on a comet approaching earth. The distance, g(x) in kilometers, of the…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: S(x) = 12-r- 12 nat is the minimum or maximum of f(x) (put "0" if there is no minimum or maximum or…

A: As per given by the function, find the minimum or maximum of fx The given function is, fx=x2-x-12…

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Q: Question Find the maximum value of the function f(x, y) = ry subject to the constraint r+y2 =40.

A: see 2nd step

Q: A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the…

A: Step1 (b) g(x)= 250,000cosec(π/24x) g(4)= 250,000cosec(π/24*4) = 250,000cosec(π/96) =…

Q: 5. Find the absolute minimum value and the absolute maximum value of y = x3 – 6x² + 9x + 3 on the…

A:

Q: (x² – 4)? attain the absolute maximum For what value of x does the function g(x) in the interval…

A: First find the derivative of function then draw the wavy curve and check derivative goes positive…

Q: Find the maximum value of f(x, y) = 2x²y³ +5 on the unit circle. (Give an exact answer. Use symbolic…

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Q: f(x) =|x - 5|+2 Find the minimum on the interval [-3, 7]

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: We have to find minimum time in hours.

Q: Minimizing Costs Suppose the cost per hour incurred in operating a cruise ship is 6a + b²v³ dollars…

A: Given that, the cost per hour incurred in operating a cruise ship is 6a+b2v3 dollars per hour. It is…

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A: Given: Cx=x2-4000x+50

Q: Find the extreme values of f(x,y) = xy subject to the constraint x +y - 6 = 0. The extrema are (Use…

A: Find the extrema

Q: tion Find A and B given that the function y = A + Ba has a minimum value of 54 at x = 81. a) OA= 486…

A:

Q: Find the values of constants a, b, and c so that the graph of y = ax + bx + cx has a local maximum…

A: Consider the provided question,

Q: Find the minimum value of f(x,y,z) = x² + y² +z² subject to - 8x - 4y + 2z = -84. The value of f at…

A: We use Lagrange multipliers method for optimization to solve the given question.

Q: Find the dimensions of a rectangle that has area 64 sq.ft. such that perimeter is a minimum.…

A: Area of rectangle = 64 Let Length be x ft. Width = 64/x Perimeter  P=2l+b  =2x+64x

Q: Set f(x) = - 3æ? 12x + 4. 1. Rewrite f(x) in vertex form a(x – h)² + k. f(x) 2. The vertex of f(x)…

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Q: f(x, y) = 3x?y, x? + y4 = 5 maximum value 48 minimum value -48

A:

Q: 2 Using calculus techniques find the absolute maximum(s) and absolute minimum(s) of f(z) = 13 - 2r²…

A: To find the critical numbers we try to solve f'(x)=0 So there are no critical numbers.

Q: 51. Investing. Gina has just invested in two funds. The combined value V, in dollars, of the two…

A: Find your answer below

Q: the absolute maximum value of g: 88 and the absolute minimum value of g: -15(nin mu mutlakee l

A:

Q: Find the absolute maximum and absolute minimum values of fon the given interval. 2 – 64 F(x) = [-64,…

A: Given  ( fx ) = x2-64x2+64 ( fx ) = 0  ddx x2-64x2+64 = 0 By quotiest rule :- ddx…

Q: The function y = a. O a-3 O a = -2 ax4 ++has a minimum at the point (√(√)). D . Determine the value…

A: To find the minimum point of the function

Q: Minimizing Costs Suppose the cost per hour incurred in operating a cruise ship is 6a + b?v³ dollars…

A: Given:-                 Suppose the cost per hour incurred in operating a cruise ship is 6 a + b 2 v…

Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 40 and P =…

A: Given that    Three positive numbers x,y and z                The sum of these numbers is 40.…

Q: Find the maximum value and the minimum value of the function and the values of x and y for which…

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Q: Find the maximum value of f(x, y) = 2x²y³ + 7 on the unit circle. (Give an exact answer. Use…

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Q: A gift box is made in the shape of a triangular prism. The triangular end is an equilateral triangle…

A: