Consider the function. f(x, y) = 3(y + 1)x² Identify the point(s) on the graph of fat which the tangent plane is horizontal. (3,0) (0, y) for all y (0, 3) (x, 0) for all x O (x, 0) for only x ≥ 0

Q: Where are the relative extrema (local maximum and minimum) on the curve? y = 3x² – x A. (0, 0) only…

A: given curve is y=3x2-x3 find the local maxima and local minima

Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

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Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

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Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

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Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

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Q: Let f (x, y) = e(3x-4y). Find the equation for the tangent plane to the graph of f at the point (1,…

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Q: Find the extrema of f(x,y) = xy + 2x2y. Classify the points as a max, min, or saddle  Thank you for…

A: Given:fx,y=xy+2x2y. We have to find the extrema and also classify the points as max, min, or saddle.