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Question :
201) Find the direction in which the function increasing most : 1757201

201) Find the direction in which the function is increasing most rapidly at the point P0.

f(x, y) = xey - ln(x), P0(-3, 0)

202) Find the direction in which the function is increasing most rapidly at the point P0.

f(x, y, z) = xy - ln(z), P0(1, -2, 2)

203) Find the direction in which the function is increasing most rapidly at the point P0.

f(x, y, z) = x y^{2} + z^{2}, P0(1, 1, 2)

204) Find the derivative of the function f(x, y) = x^{2} + xy + y^{2} at the point (-7, -6) in the direction in which the function increases most rapidly.

A) B) C) D) 3

205) Find the derivative of the function f(x, y) = x^{2} + xy + y^{2} at the point (6, 7) in the direction in which the function decreases most rapidly.

A) - B) - C) - D) -3

206) Find the derivative of the function f(x, y) = exy at the point (0, -5) in the direction in which the function increases most rapidly.

A) 15 B) 10 C) 5 D) 6

207) Find the derivative of the function f(x, y) = exy at the point (0, 3) in the direction in which the function decreases most rapidly.

A) -3 B) -9 C) -6 D) -2

208) Find the derivative of the function f(x, y) = tan-1 y/x at the point (4, -4) in the direction in which the function increases most rapidly.

209) Find the derivative of the function f(x, y) = tan-1 y/x at the point (5, -5) in the direction in which

the function decreases most rapidly.

210) Find the derivative of the function f(x, y, z) = ln(xy + yz + zx) at the point (5, 10, 15) in the direction in which the function increases most rapidly.