For a function of two variables, describe relative minimum.

BenoguigoliB

BenoguigoliB

Answered question

2021-02-17

For a function of two variables, describe relative minimum.

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2021-02-19Added 104 answers

Let f be a function with two variables with continuous second order partial derivatives f×,fyy and fxy at a critical point (a,b).
The necessary condition for the minimum of the function is fx=0 and fy=0 at critical point (a, b).
And the sufficient condition is,
Let,
D=f×(a,b)fyy(a,b)fxy2(a,b)
If D>0 and f×(a,b)>0, then f has a relative minimum at (a,b).

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