Find all points ( x , y ) where 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 ) = 8 x y + 8 y 2 − 2 x + 2 y − 1
Find all points ( x , y ) where 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 ) = 8 x y + 8 y 2 − 2 x + 2 y − 1
Solution Summary: The author explains that the function f(x,y)=8xy+8+y2-2x+2y-1 has a possible relative maximum or minimum, and the nature of
Find all points
(
x
,
y
)
where
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
)
=
8
x
y
+
8
y
2
−
2
x
+
2
y
−
1
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 .
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.