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Locate all relative minima, relative maxima, and saddle points, if any? what's the answer and how/why?

f(x,y) = e^-(x^2 + y^2 + 14x)

f has a:

A.) relative minimum

B.) relative maximum

C.) saddle point

D.) is inconclusive

at the point ( ??? , ??? )

TYIA

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1 Answer

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  • 4 months ago
    Favorite Answer

    f_x = (2x + 14)*e^[-(x^2 + y^2 + 14x)].

    f_y = (2y)*e^[-(x^2 + y^2 + 14x)].

    The point of interest is (-7,0), where both partial derivatives are zero.

    At (-7,0), the value of f_y switches from negative to positive as y grows.

    At (-7,0) the value of f_x also switches from negative to positive as x grows.

    So there's a minimum at (-7,0).  No other max, min, or saddle points.

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