Question

the extreme value of f (ab) is said to the maximum value at (ab) if the difference f(x,y) -f (a,b) is​

Answer 1

Answer:

The extreme values of a function f , set f'(x)=0.

Step-by-step explanation:

From the above question,

To determine the real valued function f(x, y) is said to be continuous at point (a, b).

A function f(x, y) is said to be continuous at point (a, b) of its domain of definition if,

           f(x,y) = f(a,b)

In other words a function f(x, y) is said to be continuous at point (a, b) of its domain of definition if for ε > 0 there exists a neighbourhood N of

(a, b) such that.

The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.

To find extreme values of a function f , set f'(x)=0 and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.

| f(x, y) - f(a, b) | < ε for all (x, y) ∈ N

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Answer 2

Answer:

The extreme values of a function f, f’(x)=0 . Differentiate the function at x and gives value =0

Step-by-step explanation:

Firstly we know about the Extreme value theorem :

The extreme value theorem states That if a real valued function F is continuous on the closed interval (a,b) , then F must attain a maximum and a minimum each at least once. That is there exist Numbers c and d in closed interval (a,b) such that

F(c)≥ F(x)≥ F(d). For every x belongs to closed interval (a,b)

Now we consider the question,

To determine the real valued function f(x,y) Is said to be continuous at point (a,b).

A function f(x,y) Is set to be continuous at point ( a, b) if its domain by definition

f(x,y)=f(a,b)
In other words, a function f(x,y) Is said to be continuous at point (a,b) if its domain for ∈ grater than zero there exists a neighbourhood N of (a,b) Such that .

Now we applied here the extreme value theorem,

To Find extreme value of a function f,

Set f’(x)=0 and solve it. This gives you the X coordinates of the extreme values or local maximums and minimums.

( f(x,y)- f(a,b) ) less than ∈ for all (x,y) belongs to N

Means that Differentiate the Function at x and gives the value =0.

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