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Let f(x, y) = x^2 + 2xy + 5y^2 + 2x + 10y - 3. At which point(s) does f(x, y) have possible maximum

Question : Let f(x, y) = x^2 + 2xy + 5y^2 + 2x + 10y - 3. At which point(s) does f(x, y) have possible maximum : 2163361

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) Let f(x, y) = x2 + 2xy + 5y2 + 2x + 10y - 3. At which point(s) does f(x, y) have possible maximum/minimum values?

A) (-1, 17) and (0, 5)

B) (1, 0)

C) (-1, 0) and (0, 1)

D) (0, -1)

E) none of these

2) Let f(x, y) = 5x2 - 5y2 + 2xy + 34x + 38y + 12. At which point does f(x, y) have a possible maximum or minimum value?

A) (4, 3)

B) (4, -3)

C) (-4, 3)

D) (-4, -3)

3) Let f(x, y) = yex + xy2. At which point does f(x, y) have a possible maximum or minimum value?

A) ((√(2)/2), - (√(2)e√(2)/2/2))

B) ((1/2), -e1/2)

C) (0, 0)

D) ((1/2), - (e1/2/2))

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

4) Find all points (x, y) where f(x, y) = 3xy - x2 - y2 - 2x - y + 3 has a possible relative maximum or minimum.

Enter your answer as just (a, b) where a, b are reduced fractions of form (c/d).

5) Find all points (x, y) where f(x, y) = x2 - 2y2 + 4x - 6y + 8 has a possible relative maximum or minimum.

Enter your answer as just (a, b) where a, b are either integers or reduced fractions of form (c/d).

6) Find all points (x, y) where f(x, y) = 2x2 + 2y3 - x - 6y + 14 has a possible relative maximum or minimum.

Enter your answer exactly as just (a, b), (c, d) with b > d and where a, b, c, d are either integers or reduced fractions of form (e/f).

7) Find all points (x, y) where f(x, y) = x3 - y2 - 3x + y + 5 has a possible relative maximum or minimum.

Enter your answer exactly as just (a, b), (c, d) with a > c and where a, b, c, d are either integers or reduced fractions of form (e/f).

8) Find all points (x, y) where f(x, y) = x2 + y3 - 6y2 + 6x - 15y has a possible relative maximum or minimum.

Enter your answer exactly as just (a, b), (c, d) with b < d and where a, b, c, d are all integers.

9) Find all points (x, y) where f(x, y) = x2 + xy + y2 - x - y + 2 has a possible relative maximum or minimum.

Enter your answer exactly as just (a, b) where a, b are reduced fractions of form (c/d) or integers.

10) Find all points (x, y) where f(x, y) = xy - 2x2 + x - 4y + 1 has a possible relative maximum or minimum.

Enter your answer exactly as just (a, b) where a, b are either reduced fractions of form (c/d) or integers.

11) Let f(x, y, z) = x2y + (x/z). Find (∂f/∂z).

Enter your answer as a polynomial in x in standard form (unlabeled).

12) Let f(x, y, z) = ex^2 + y^2 + z^2. Find (∂f/∂z).

Enter your answer as a polynomial in ex^2 + y^2 + z^2 in standard form (unlabeled).

13) Let f(x, y) = √(x2 + y2). Compute (∂f/∂x) at (3, 4).

Enter just a reduced fraction (a/b).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

14) Let f(x, y) = x4 - y2 + 3x2 + 2y - 7. The first partial derivatives of f(x, y) are zero at the points (0, 1) and (-1, 1). Use the second derivative test to determine the nature of f(x, y) at each of these points.

A) (0,1) neither relative maximum nor minimum, (-1, 1) maximum

B) (-1, 1) relative maximum, (0, 1) neither relative maximum nor minimum

C) (0, 1) relative maximum, (-1, 1) relative minimum

D) (0, 1) no conclusion possible, (-1, 1) minimum

E) none of these

15) Find all points (x, y) where f(x, y) = x2 + xy + y2 - 3x + 2 has a possible relative maximum or minimum. Use the second-derivative test to determine, if possible, the nature of f(x, y) at each of these points.

A) (-2, 1) is a relative maximum

B) (-2, 1) is a relative minimum

C) (2, -1) is a relative maximum

D) (2, -1) is a relative minimum

16) Find all points (x, y) where f(x, y) = x3 - 12y + y2 has a possible relative maximum or minimum. Use the second-derivative test to determine, if possible, the nature of f(x, y) at each of these points.

A) (0, 0) gives a relative maximum

B) Test Inconclusive

C) (0, 6) gives a relative maximum

D) (0, 0) gives a relative minimum

17) Find all points (x, y) where f(x, y) = (1/x) + xy - (1/y) has a possible relative maximum or minimum. Use the second-derivative test to determine, if possible, the nature of f(x, y) at each of these points.

A) (1, 1) gives a relative minimum point

B) Neither a relative maximum nor a relative minimum at (-1, 1)

C) (-1, 1) gives a relative minimum point

D) (-1, 1) gives a relative maximum point

Solution
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