21.2k views
11 votes
Suppose that

f
(
x
,
y
)
=
x
+
5
y
f
(
x
,
y
)
=
x
+
5
y
at which

1

x

1
,

1

y

1
-
1

x

1
,
-
1

y

1
.

Absolute minimum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Absolute maximum of
f
(
x
,
y
)
f
(
x
,
y
)
is

Suppose that f ( x , y ) = x + 5 y f ( x , y ) = x + 5 y at which − 1 ≤ x ≤ 1 , − 1 ≤ y-example-1
User SciPhi
by
8.7k points

1 Answer

7 votes

Answers:

  • Absolute min = -6
  • Absolute max = 6

========================================================

Step-by-step explanation:

The range of x values is
-1 \le x \le 1 which means x = -1 is the smallest and x = 1 is the largest possible.

Similarly the smallest y value is y = -1 and the largest is y = 1.

----------

Plug in the smallest x and y value to get

f(x,y) = x+5y

f(-1,-1) = -1+5(-1)

f(-1,-1) = -6

Therefore, the absolute min is -6

----------

Now plug in the largest x and y values

f(x,y) = x+5y

f(1,1) = 1+5(1)

f(1,1) = 6

The absolute max is 6

User Akrun
by
7.9k points

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