For the following exercises, find the critical points of the function by using algebraic techniques (completing the square) or by examining the form of the equation. Verify your results using the partial derivatives test. 316. f ( x , y ) = x 2 + y 2 + 2 x − 6 y + 6
For the following exercises, find the critical points of the function by using algebraic techniques (completing the square) or by examining the form of the equation. Verify your results using the partial derivatives test. 316. f ( x , y ) = x 2 + y 2 + 2 x − 6 y + 6
For the following exercises, find the critical points of the function by using algebraic techniques (completing the square) or by examining the form of the equation. Verify your results using the partial derivatives test.
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?