Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y
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- Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at (12,12,12) be maximumFind the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an angle of π/6 from horizontal.Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the point (π/2, π2/4).
- Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0Fat (12,12,12) be maximum?Find a unit vector tangent to the curve of intersection of -x^2 - 2y^3 = z - 3 and 25/x2 - 4y - 3z^2 = - x + 6 at the point (1,1,0).4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.
- Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.2.b) Which vector is not normal at the plane defined by 2x - 4y-6z+1=0?Suppose L(5, 4) was reflected across the line y = x then translated along the vector <4, 0>. What is the y-coordinate of L''?
- Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional derivative of ƒ at ⟨9, 9⟩ in the direction of the vector w.Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25 and y2+z2=20 at the point (3, 4, 2).Find a vector equation for the curve of intersectionof the surfaces x^2 + y^2 = 4 andz = xy.