Find the maximum and minimum of f(x,y) = yx2 + y(y - 1)2 subject to x2 + y2 =1.

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Q: f(x, y, z) = x-y y²+2y+z²-4

A: We have shown that the domain is all of R3 except the points on the surface of infinite length…

Q: Suppose the cost and revenue functions of a company are R(x) = 60x and C(x) = 360 + 40x + 0.1 x²…

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Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

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Q: Describe two methods for optimizing a function z = f (x, y) subject to a constraint.

A: Optimization is the method to find the local minima or maxima of a function. If there are…

Q: f (x) = x2 – 2x + 2 | P 3 3+h an expression for the gradient of the line joining the points, P and…

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Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

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…

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Q: What is the x-component of the minimum point of the function in the picture?

A: Given  z=x2+xy+y2-y ∂z∂x=2x+y On putting,  ∂z∂x=0 ⇒2x+y=0 ---> eqn(1) Now, ∂z∂y=x+2y-1 On…

Q: A cubie function has rule x) ax+ br + 6. The points (1,4) and (2, 11) lie on the graph of y f().…

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Q: Let f(x, y) = = 160 - 2x² - 4y² For which value(s) of y is f(-3, y) = 7? y =

A: Given function

Q: nd the point (x, y) at which the line f(x) = 5x + 11 intersects the line g(x) = -2x-3

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Q: Find the dimensions of the rectangle of maximum area having two vertices on the x-axis and 2…

A: Let the rectangle has its two vertices on x-axis and remaining two vertices on the parabola y=4-x2.…

Q: Which point on the curve y = √x - 4+9 is closest to the point (7, 9)? (x, y) = ( What is this…

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Q: A competitive firm's profit is given by T(x,.x2) = 95(4x2 + 6x}")- 4.75x, - 15x2. %3D The stationary…

A: To find stationary point of a function fx,y, we have to find fx and fy. Then we put fx=0 and fy=0.…

Q: f(x)=2-\x t4| give their domain, range, -intercept, and y-intercept

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Q: f(x) = xª -4 and Perpendicular to the line x - 4y + 1= 0.

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Q: Sketch the domain of f(x, y) = √4x² - y² x - y² on the ry-plane.

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Q: F(x)= 4x6- 7x5 find local minimum

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

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Q: Find an sketch the domain of f(x,y)= 16x² – x² –4y². -

A: Given that fx,y=16x2-x2-4y2 To determine the domain of the function. fx,y is only defined for…