Find and classify all the extrema of the function f(x; y) = Exp(-x2 -y2 )*(x2 +...

Find and classify all the extrema of the function
f(x; y) = Exp(-x² -y² )*(x² + 2y²).

Expert Solution

milcah answered 2 years ago

Use Lagrange multipliers to find the absolute extrema of f(x,y) = x2 + y2 - 2x...

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Find and classify the local extrema of the function f(x,y) = (x^3)y+12(x^2)+16(y^2).

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j + (3 + x) k . Let a > 0 and let S be part of the spherical surface x2 + y2 + z2 = 2az + 15a2 that is above the x-y plane and the disk formed in the x-y plane by the circular intersection between the sphere and the plane. Find the flux of F outward across S.

Curvilinear integral of the function f (x, y) = x2 + y2 on a (3,0) centered...

Curvilinear integral of the function f (x, y) = x2 + y2 on a (3,0) centered and 3 radius circle. a)Calculate the curvilinear integral by expressing the curve in parametrically. b)Calculate the curvilinear integral by expressing the curve in polar coordinates. c)Calculate the curvilinear integral by expressing the curve in cartesian coordinates.

a) For the function f (x) = x – exp(−x2), do a calculation by hand using...

a) For the function f (x) = x – exp(−x2), do a calculation by hand using a calculator to find the root to an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy. b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of Newton’s method (by hand); tabulate the result.

Find the local extrema of the following function. f(x,y)=108+7xy-5x2-6y2

For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any relative extrema...

For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any relative extrema or saddle points. Use the D test to classify. Give your answers in (x,y,z) form. Use factions, not decimals.

The value of f depends on two independent variables x and y as defined below: f(x,y)=x2+y2−x+3cos(x)sin(y)...

The value of f depends on two independent variables x and y as defined below: f(x,y)=x2+y2−x+3cos(x)sin(y) Function f has a minimum in the neighborhood of the origin (i.e. [0 0]). Find x and y which minimize f. Note: You are not allowed to use MATLAB built-in functions for optimization. Follow the logic of the derivative test: The minimum of f occurs where: ∂f∂x=0∂f∂y=0

find fx, fy and fz for the following function: f(x,y,z) = (xz/1-x2-y2)-3/4 if you can show...

find fx, fy and fz for the following function: f(x,y,z) = (xz/1-x2-y2)-3/4 if you can show working for the partial derivatives would be great thanks, Ben.

1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is...

1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is of a fraction format) : a. has a stationary point at (1, 0) b. has a stationary point at (0, 0) c. has a stationary point at (0, 1) d. has no stationary points 2. Which of the following functions don’t have unit elasticity at P = 6? a. Demand: Qd = 24 - 2 P b. Demand: Qd = 10/P c. Demand: log...

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