# How do you minimize and maximize #f(x,y)=x-y/(x-y/(x-y))# constrained to #1<yx^2+xy^2<16#?

See below.

This problem can be successfully handled with the Lagrange Multipliers technique.

The local maxima/minima points are

Attached a plot showing the feasible region superimposed to the objective function level curves, with the local maxima/minima points.

By signing up, you agree to our Terms of Service and Privacy Policy

To minimize and maximize ( f(x,y) = \frac{x - y}{x - \frac{y}{x - \frac{y}{x - y}}} ) subject to the constraint ( 1 < yx^2 + xy^2 < 16 ), you would first find the critical points of ( f(x,y) ) within the given constraint. Then, evaluate the function at those critical points and at the endpoints of the constraint interval to determine the minimum and maximum values of ( f(x,y) ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How fast is the radius of the basketball increasing when the radius is 16 cm if air is being pumped into a basketball at a rate of 100 cm3/sec?
- How do you find the linearization of #f(x) = x^4 + 5x^2# at a=-1?
- How do you find the linearization of the function #z=xsqrt(y)# at the point (-7, 64)?
- A hypothetical square shrinks so that the length of its diagonals are changing at a rate of −8 m/min. At what rate is the area of the square changing when the diagonals are 5 m each?
- A plane flying horizontally at an altitude of 1 mi and a speed of 540 mi/h passes directly over a radar station. How do you find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7