3: Let u(x, y) and v(x, y) be two twice differentiable functions such that ux = Vy, Uy Show that u(x, y) has also a saddle point at P. Hint: First, show that P is a critical point of u(x, y) and then apply 2nd derivatiyę test. = -Vg and v(x, y) has a saddle point at some P.

Q: 3. f(x, y) = 5x¹ − 4x5 + 5y¹. Ans.: local minimum 0 at (0, 0), saddle at (1,0)

A: 3. Given that the function                          f(x, y)=5x4-4x5+5y4.

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Q: An image is projected onto a wall, and the irradiance of the light on the wall is (3) given by f(x,…

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Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

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Q: 4. Find the locations (x, y) AND function values f(x, y) for all relative extrema and saddle points…

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Q: Find the extrema and/or the saddle points of the functions a) f(x, y) = ex cos y b) f(x, y) = x² +…

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Q: A) Find and classify the critical points of f(z, y) = x³ + y3 – 6y? – 3.x + 9 using the first and…

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Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

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Q: The gradient of f(x, y) = ² * sin(2y) at (x, y) = (2, 1) is defined as followed: Vf(x, y) = (fz(2,…

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Q: Let f(x, y, z) = xyz Find the direction in which the function increase most rapidly at the point…

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Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)…

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