Question

8. The necessary conditions for a function f(x,y) to have extremum at(a,b) is​

Answer 1

Answer:

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Answer 2

Answer:

The necessary conditions for a function f(x,y) to have extremum at(a,b) is​: The derivative of the function f(x,y) is zero at the point (a,b).

Step-by-step explanation:

• Condition for extremum: The derivative of any function will be zero or  will not be exist at the extreme point. Extremum is one of the critical points.

        Example: any function, f(x) = x³ - 12x , here x =2 is extreme point.

                        reason ⇒  f'(x) = 3x² - 12

                                         at x=2, f'(2) = 12 - 12 = 0

• Exception: Suppose a function f(x) = x²

                           The derivative f'(x) = 2x

                            At x=0, f(x) = 0, but this point is not extremum.

• Critical points: The derivative of a function becomes zero or does not exist at a point, then that point is called critical point.