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Find a degree 
Magazine Problem 3
Use the tangent plane approximation to estimate $$ \Delta z=f(a+\Delta x, b+\Delta y)-f(a, b) $$ for the given function at the given point and for the given values of \(\Delta x\) and \(\Delta y\) $$ f(x, y)=x^{2} y^{3},(a, b)=(3,2), \Delta x=0.1, \Delta y=-0.1 $$
Problem 3
Solve using Lagrange multipliers. Maximize \(f(x, y)=-x^{2}+x y-4 y^{2}\) subject to the constraint \(x+y+4=0\)
Problem 3
In Exercises 1 through 20 , find all critical points, and determine whether each point is a relative minimum, relative maximum. or a saddle point. $$ f(x, y)=-x^{2}+x y-y^{2}+3 x+8 $$
Problem 3
Find both first-order partial derivatives. Then evaluate each partial derivative at the indicated point. $$ f(x, y)=x^{2} y-x^{3} y^{2}+10,(1,2) $$
Problem 3
Evaluate the function at the indicated points. $$ f(x, y)=2 x^{2}+y^{2}-4,(1,2),(2,-3),(-1,-2) $$
Problem 4
Use the tangent plane approximation to estimate $$ \Delta z=f(a+\Delta x, b+\Delta y)-f(a, b) $$ for the given function at the given point and for the given values of \(\Delta x\) and \(\Delta y\) $$ f(x, y)=x^{3} y^{4},(a, b)=(-1,1), \Delta x=0.1, \Delta y=-0.2 $$
Problem 4
Solve using Lagrange multipliers. Maximize \(f(x, y)=-5 x^{2}-x y-y^{2}\) subject to the constraint \(x+y+20=0\)
Problem 4
Find both first-order partial derivatives. Then evaluate each partial derivative at the indicated point. $$ f(x, y)=x y-x^{2} y^{3}+y^{4},(1,-1) $$
Problem 4
Evaluate the function at the indicated points. $$ f(x, y)=x^{2}+x-y^{2},(2,3),(-1,4),(-2,-3) $$
Problem 4
In Exercises 1 through 20 , find all critical points, and determine whether each point is a relative minimum, relative maximum. or a saddle point. $$ f(x, y)=-5 x^{2}-x y-y^{2}-4 x-8 y $$
