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 ) = 2 x 2 + y 3 − x − 12 y + 7
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 ) = 2 x 2 + y 3 − x − 12 y + 7
Solution Summary: The author explains that the function f(x,y) = 2x2+ y3-x-12y+7 has a possible relative maximum or minimum, and
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
)
=
2
x
2
+
y
3
−
x
−
12
y
+
7
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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