A function is defined on R2 as: f(x,y)= 2x3 -6xy + 2xy2 +2 a) Find any...
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A function is defined on R2 as: f(x,y)= 2x3 -6xy + 2xy2 +2 a) Find any critical/stationary points of the function f. b) Determines whether these points are local minimum, local maximum or saddle point. c) Find the gradient of the function f at the point (x,y)=(1,1). d) Find the directional derivative of f at the point (x,y)=(1,1) in the direction given by the vector v = [1,2]. e) Find a formula for the tangent plane to the function through the point (x,y,z)=(1,1,0). f) Use the formula for the tangent plane (linearizationa) at the point (x,y,z)=(1,1,0) to estimate f (1.1,0.8). g) Draw the graph of the function in Matlab for -4sx ≤4, -4sy≤4. A function is defined on R2 as: f(x,y)= 2x3 -6xy + 2xy2 +2 a) Find any critical/stationary points of the function f. b) Determines whether these points are local minimum, local maximum or saddle point. c) Find the gradient of the function f at the point (x,y)=(1,1). d) Find the directional derivative of f at the point (x,y)=(1,1) in the direction given by the vector v = [1,2]. e) Find a formula for the tangent plane to the function through the point (x,y,z)=(1,1,0). f) Use the formula for the tangent plane (linearizationa) at the point (x,y,z)=(1,1,0) to estimate f (1.1,0.8). g) Draw the graph of the function in Matlab for -4sx ≤4, -4sy≤4.
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a To find the criticalstationary points of the function fx y we need to find the points where the gr... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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