Answer with Step-by-step explanation:
We are given that


We have to find the extreme values of the function.



Therefore,




Substitute the values in g(x)
Then, we get





When
then,

When 
Then, 


Hence, maximum value of f(x,y,z) is 23 at (2,2,1) and minimum value of f(x,y,z) is -23 at (-2,-2 ,-1).
The time in the exactly in the middle would be 9:30AM
Given
- f(n) values for n=1,2,3,4
- possible candidates for the function
Solution:
Method: Evaluate some of the values, for each function. A function with ANY value not matching the given f(n) values will be rejected.
N=1, f(n)=4
f(1)=4-3(1-1)=4
f(1)=4+3^(1+1)=4+3^2=4+9=13 ≠ 4 [rejected]
f(1)=4(3^(n-1))=4(3^0)=4
f(1)=3(4^(n-1))=3(4^0)=3*1=3 [rejected]
N=2, f(n)=12
f(1)=4-3(2-1)=4-3(1)=1 ≠ 12 [rejected]
[rejected]
f(1)=4(3^(2-1)=4*3^1=4*3=12
[rejected]
Will need to check one more to be sure
N=3, f(n)=3
[rejected]
[rejected]
f(3)=4(3^(n-1))=4(3^(3-1))=4(3^2)=4*9=36 [Good]
[rejected]
Solution: f(n)=4(3^(n-1))
Using continuity concepts, the answers are given by:
- The function is right-continuous at x = 0.
- The function is left-continuous at x = 1.
------------------------------------
A function f(x) is continuous at x = a if:

- If
, the function is left-continuous. - If
, the function is right-continuous. - For the given function, the continuity is tested at the points in which the definitions are changed, x = 0 and x = 1.
------------------------------------
At x = 0.
- Approaching from the left, it is less than 0, thus:

- Approaching from the right, it is more than 0, thus:


- Since
, the function is right-continuous at x = 0.
------------------------------------
At x = 1.



- Since
, the function is left-continuous at x = 0.
A similar problem is given at brainly.com/question/21447009