Asked by Becky
If a function of one variable is continuous on an interval and has only one critical number, then a local maximum has to be an absolute maximum. But this is not true for functions of two variables. Show that the function
f(x,y)= 3xe^y − x^3 − e^(3y
)has exactly one critical point, and that f has a local maximum there that is not an absolute maximum.
f(x,y)= 3xe^y − x^3 − e^(3y
)has exactly one critical point, and that f has a local maximum there that is not an absolute maximum.
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