The function $f ( x , y ) = e ^ { - ( x - a ) ^ { 2 } - ( y - b ) ^ { 2 } }$ where a and b are constants is sometimes referred to as a "bump function" and is used to construct functions which take on maximum values at certain points.Show that f(x, y)has a maximum at (a, b).

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The Answer of The function $f ( x , y ) = e ^ { - ( x - a ) ^ { 2 } - ( y - b ) ^ { 2 } }$ where a and b are constants is sometimes referred to as a "bump function" and is used to construct functions which take on maximum values at certain points.Show that f(x, y)has a maximum at (a, b).

The Function f(x,y)=e−(x−a)2−(y−b)2f ( x , y ) = e ^ { - ( x - a ) ^ { 2 } - ( y - b ) ^ { 2 } }f(x,y)=e−(x−a)2−(y−b)2

The Function $f ( x , y ) = e ^ { - ( x - a ) ^ { 2 } - ( y - b ) ^ { 2 } }$