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Practice for classifying critical points

Related Topics

Wize University Calculus 2 Textbook > Multivariable Functions

Max & Min

5 Activities

A function f(x,y)f(x, y)is found to have the following critical points (listed in the first column). The second derivative test function, D, is defined as:


D(x,y)=3x22y−9xy2x−2yD(x, y) = \dfrac{3x^22y -9xy}{2x-2y}

and the second derivative with respect to x is given as:

fxx=3y−xx−yf_{xx} = \dfrac{3y-x}{x-y}
Classify each as a local minima, maxima, or saddle point
(-11, 1)
(-11, -9)
(7, 2)
(3, -4)
More Max & Min Questions:
Critical Points
Practice
Find and classify all the critical points for f(x, y)=(y−2)x2−y2f(x,~y)=(y-2)x^2-y^2.
Lagrange Multipliers
Practice
Find the maximum and minimum values of f(x, y, z)=3x2+yf(x,~y,~z)=3x^2+y subject to 4x−3y=9 and x2+z2=94x-3y=9~\text{and}~x^2+z^2=9.