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 disc
riminant 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 answer:
Answer:
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:
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you seem to want to know the value of f(0). Put 0 where x is, then evaluate.
The initial value of the function is 3.
_____
You will observe that when x=0, the exponential term evaluates to 1. This is true regardless of its base. Thus f(0) is always the coefficient of the exponential term—in this case, 3.