F(x, y)=x^2+y^2-6x-6y+41. how many critical points does g have in r22. if there is a local minimum, what is the value of the discriminant d at that point? 3. if there is a local maximum, what is the value of the discriminant d at that point? 4. if there is a saddle point, what is the value of the discriminant d at that point? 5. what is the maximum value of f in r2? 6. what is the minimum value of f in r2?

1) There is only a critical point at (3,3).

2) If there is a local minimum, the value of the discriminant must be D>0

3) If there is a local maximum, the value of the discriminant must be D>0

4) If there is a saddle point, the value of the discriminant must be D<0

5) There is not a local maximum of f

6) There is a local minimum at (3,3). f(3,3)=23

Step-by-step explanation:

We have the fuction:

Its partial derivatives are:

When

0=2x-6 ⇒ 2x=6 ⇒x=3

When

0=2y-6 ⇒ 2y=6 ⇒y=3

The critical point is (3,3)

Its second order derivatives are:

The value of the discriminant is

=2×2-0=4

As D>0 and , there is a local minimun at (3,3)

The value of f(x,y) at (3,3) is:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.