Question

PM
1 marks)
If A = fxx(a,b), B = fxy(a,b) and C = fyy(a, b)
then f(x,y) will have a minimum value
at (a, b) if​

Answer 1

Step-by-step explanation:

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Answer 2

f(x,y) will have a minimum value at (a, b) if​ $AC-B^{2} > 0$ and $A > 0$.

• In two-variable calculus, a two-variable twice differentiable function can have maxima and minima at some points.
• To find these extreme points, we need to calculate $A=f_{xx}$, that is the twice partial derivative of f with respect to x, $B=f_{xy}$, that is the partial derivative of f with respect to x and then another partial derivative of $f_{x}$ with respect to y, and $C=f_{yy}$, that is the twice partial derivative of f with respect to y.
• Now, if the value of the expression $AC-B^{2}$ at the point of investigation (a, b) is greater than 0, and the value of $A=f_{xx}$ at the point of investigation (a, b) is greater than 0, the function f(x, y) will have a minimum value at the point of investigation (a, b).

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