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:

666666666666666666666

6

6

6

6

6

6

6

66

6

6

6

66

6

66answer:

step-by-step explanation:

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,