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 4 − 12 x 2 − 4 x y − y 2 + 16
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 4 − 12 x 2 − 4 x y − y 2 + 16
Solution Summary: The author explains that the function f(x,y) has a possible relative maximum or minimum, and the nature of
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
4
−
12
x
2
−
4
x
y
−
y
2
+
16
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 .
Let f(x) = x2. Give an
equation of the line that intersects the graph of f(x) at x = 0 and x =
V2.
The wave heights h in the open sea depend on the speed v of the wind and the length of time t that
the wind has been blowing at that speed. Values of the function h=f(v,t), are recorded in feet in the
following table. Use the table to find a linear approximation to the wave height function when v is
near x knots and t is near 20 hours. Then estimate the wave heights when the wind has been blowing
for 24 hours at y knots where x and y values given by above table.
Wind speed (knots)
V
20
t
30
40
50
60
5
5
9
14
19
24
10
7
13
21
29
37
Duration (hours)
15
8
16
25
36
47
20
8
17
28
40
54
30
9
18
31
45
62
40
9
19
33
48
67
50
9
19
33
50
69
Find all points (x, y) where the functions f(x), g(x), h(x) have the same value:
f (x) = 2"-5
+ 3,
g(x) = 2x – 5,
h(x)
+ 10
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