Question

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

Answer 1

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