For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. 363. f ( x , y , z ) = y z + x y , x y = 1 , y 2 + z 2 = 1
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. 363. f ( x , y , z ) = y z + x y , x y = 1 , y 2 + z 2 = 1
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints.
363.
f
(
x
,
y
,
z
)
=
y
z
+
x
y
,
x
y
=
1
,
y
2
+
z
2
=
1
PLEASE SOLVE STEP BY STEP WITHOUT ARTIFICIAL INTELLIGENCE OR CHATGPT
SOLVE BY HAND STEP BY STEP
4.- A beer at an unknown temperature is introduced into a refrigerator that has a constant temperature of 1°C. After 20 minutes, the temperature of the beer is 10°C, and after 40 minutes, the temperature of the beer is 6°C.
a) Determine the temperature at which the beer was placed inside the refrigerator.b) How long will it take for the beer to reach 2°C?
PLEASE SOLVE STEP BY STEP WITHOUT ARTIFICIAL INTELLIGENCE OR CHATGPT
SOLVE BY HAND STEP BY STEP
5.- It is known that the population of a certain community increases at a rate proportional to the number of people at any given moment. If the population doubled in 5 years:
a) How long will it take to triple?b) How long will it take to quadruple?