Find all points f ( x , y ) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f ( x , y ) at each of these points. If the second-derivative test is inconclusive, so state. f ( x , y ) = x 2 − 2 x y + 4 y 2
Find all points f ( x , y ) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f ( x , y ) at each of these points. If the second-derivative test is inconclusive, so state. f ( x , y ) = x 2 − 2 x y + 4 y 2
Solution Summary: The author explains that the function f(x,y)=x2-2xy+4
Find all points
f
(
x
,
y
)
has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of
f
(
x
,
y
)
at each of these points. If the second-derivative test is inconclusive, so state.
f
(
x
,
y
)
=
x
2
−
2
x
y
+
4
y
2
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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