Find the maximum value of z = xy2 subject to 8x2 + y2 = 1944; x > 0, y 2 0. z =

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: Find the maximum value of xy if it is required that 2x +7y = 35

A:

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Find two positive numbers x and y such that x+y=60 and xy^3 is maximum.

A:

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Suppose that f(x, y) = 4x* + 4y* – xy Then the minimum is

A:

Q: 5. y2 2x y26-x fx, y) = 4x+ 3y Minimum: Maximum: | | | | |

A: We need to find maximum and minimum values of f(x,y).

Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

A:

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Find the local minimum value of f(x, y) = 4 + a" + yl – 11ry.

A: Use double derivatives test to find local maximum or minima.

Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal distance…

A:

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum.

A: To solve the following problem

Q: Find the absolute maximum and minimum of the function f(x,y) = 7y + 64x – 3 over the closed region…

A:

Q: Find the maximum of the quantity xy2, where r and y are nonnegative re numbers, and x+y = 9. Enter…

A: x+y=9 or y=9-x and x and y are non-negative real numbers

Q: Find the absolute maximum of f(x,y) = 7x²y² + 5y² + 9x² bounded by y = x, y = 0 and x = 2.

A:

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

A:

Q: Find 3 numbers x, y, and z such that their sum is 32 and P=xy^2z is a maximum.

A:

Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

A:

Q: Find the relative maxima or minima. Maximum of ƒ(x, y) = 12xy - x2 - 3y2, subject to x + y = 16

A: f(x,y)=12xy-x2-3y2 , subject to x+y=16

Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

A:

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Find the extreme values of g(x,y,z) = 2x² + xy + 4y² + xz + z² + 2. %3D and determine whether the…

A:

Q: Find the value/s of x for which y=3x^4-4x^3+1 is maximum?

A: y=3x4-4x3+1 Differentiating with respect to x, we get dydx=34x3-43x2+0=12x3-12x2 Now to find…

Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms,…

A:

Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: Find the maximum value of ƒ(x, y) = 49 - x2 - y2 on the line x + 3y = 10.

A:

Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: Find the point where the function f(x,y, z) = x + 2y + 3z subject to the I takes on its minimum…

A: The given function is f(x,y,z)=x+2y+3z.

Q: Suppose that f(æ, y) = e-2x² – 3y² + y Then the maximum is

A:

Q: Find the minimum value ofx +y +z² given x+y+z=3a.

A:

Q: Find an equation in the form y = ax³ + bx² + cx + d_whose graph has a critical point that is a local…

A:

Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

A:

Q: Find three positive numbers x, y, and z whose sum is 21 and product is a maximum.

A: There are two different questions in the image. According to our guidelines, we can solve only one…

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x + 3y = 10.

A: Solution of given question is written in below steps.

Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

A:

Q: Suppose that f(x, y) = x² – ry + y² – 5x + 5y with x² + y? < 52. 1. Absolute minimum of f(x, y) is…

A:

Q: Of all numbers whose difference is 4, fınd the two that have the minimum product. x= y=

A: Given that  Difference of two number is 4 and we need to find the two numbers whose product is…

Q: Suppose that x and y are two positive numbers, and suppose that x + 2y = 30. Find the maximum value…

A: Given data:   The first equation is x+2y=30. The expression for the function is f(x,y)=(x+1)(y+3).…

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: Given that, The price demand function is px=70-0.25x and the cost function is Cx=0.5x2+10x+800. We…

Q: Find two positive numbers x and y such thatx + 2y 50 and (x + 1)(y+ 2) is a maximum.

A:

Q: Suppose that f(x, y) = 4x* + 4y* – 2ry Then the minimum is

A:

Q: Find the point where the function f(x,y,z) = x + 2y + 3z subject to the constraint xyz= 2 takes on…

A: Answer is in below steps.

Q: Find the absolute maximum of f(x,y) = 5x²y² + 4y² + 6x² bounded by y = x, y = 0 and x = 4. %3D…

A: The given function is: f(x,y)=5x2y2+4y2+6x2Bounded Region is:  y=x,  y=0,  x=4

Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: Find the absolute maximum value and absolute minimum value of f(x, y) = 2a2 + 2y² + 4y – 1 on the…

A:

Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…