How do you minimize and maximize #f(x,y)=x/e^(xy)+y# constrained to #1<x^2/y+y^2/x<9#?
See below.
The attached plot shows the location of stationary points. The arrows represent the gradient of the objective function (black) and the boundary (red) at each stationary point. The feasible region in blue shows also level curves from the objective function. Those results were obtained using the Lagrange Multipliers technique.
By signing up, you agree to our Terms of Service and Privacy Policy
To minimize and maximize ( f(x,y) = \frac{x}{e^{(xy)}} + y ) constrained to ( 1 < \frac{x^2}{y} + \frac{y^2}{x} < 9 ), you can follow these steps:

Find the critical points of ( f(x,y) ) by taking partial derivatives with respect to ( x ) and ( y ) and setting them equal to zero.

Test the critical points along with the boundary of the constraint region to determine which points give the minimum and maximum values of ( f(x,y) ).

Use Lagrange multipliers if necessary to handle the constraint ( 1 < \frac{x^2}{y} + \frac{y^2}{x} < 9 ).

Calculate the values of ( f(x,y) ) at the critical points and along the boundary to find the minimum and maximum values.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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 do you use Newton's method to find the approximate solution to the equation #e^x=1/x#?
 How do you find the amount of sugar in the tank after t minutes if a tank contains 1640 liters of pure water and a solution that contains 0.09 kg of sugar per liter enters a tank at the rate 5 l/min the solution is mixed and drains from the tank at the same rate?
 A feeding trough full of water is 5 ft long and its ends are isosceles triangles having a base and height of 3 ft. Water leaks out of the tank at a rate of 5 (ft)^3/min. How fast is the water level falling when the water in the tank is 6 in. deep?
 Approximate #\int_0^2(1)/(1+x^3)dx# using the Midpoint Rule, given #n=4#? Please check my work
 A rectangle with sides parallel to the axes is inscribed in the region bounded by the axes and the line x+2y = 2. How do you find the maximum area of this triangle?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7