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

question 20

Essay

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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Definitions:

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An individual who seizes and holds people against their will, typically to demand ransom or fulfill other conditions.

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Pertaining to having the intention or displaying tendencies towards self-harm that could lead to one's death.

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A device or signal for warning or alerting to danger, or the state of being suddenly aware of potential or imminent danger.

Hostage Takers

Individuals or groups who illegally seize and hold people against their will, typically to demand concessions or ransom.