For the function f(x,y)=x^2+2y^2−(x^2)y, does the critical point (−2,1) correspond to a
Given,
Critical Point: (-2, 1)
Second derivative test:
Let f(x,y) be a function of two variables for which the first and second order partial derivative are continuous on some disk containing the point (a, b).
Suppose (a,b) be critical points.
Then define
- If D>0, fxx (a, b) > 0 then f has a local minimum at (a, b).
- If D>0, fxx (a, b) < 0 then f has a local maximum at (a, b).
- If D< 0, then f has a saddle point at (a,b).
- If D=0 , then the test is inconclusive.
Find partial derivative of 
For finding the Partial derivative with respect to x, keep y variable constant and differentiate with respect to x.
Partial derivative of fx with respect to y by keeping x constant.
Partial derivative of fx with respect to x by keeping y constant.
Partial derivative of f(x) with respect to y by keeping x constant.
Partial derivative of fy with respect to y by keeping x constant.
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