f(x, y) = xy³. Does there exist a point or multiple points (x, y) = (a, b) where the following statements are both true: • The direction of maximum increase is aligned with the vector (1, 1) • The slope in the direction of maximum increase is √18 Select one: O a. There exist four points (a, b). O b. There exists one point (a, b). ○ c. There exist no points (a, b). O d. There exist two points (a, b). O e. There exist infinitely many points (a, b).

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Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: Calculate Duf(-1, 1, 1) in the direction of =--23-k for the function f(x, y, z)=-4x² + 5xy + y² + 3x…

A: Given function is f(x, y, z) = -4x2 + 5xy + y2 + 3x + 3yz - z2 - 5xz

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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