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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
1 Answer
- az_lenderLv 74 months agoFavorite 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.