Find the direction for which the directional derivative of g(x, y) = 4x – xy + 2y² at (-2, 3) is a maximum. What is the unit vector, u, for which Du is maximized, and what is the value of Dy? Select the correct answer below: V197 14 197 ' 197 u = , Du = 14 =(197 197), VT97 Du = V197 14V197 u = Du = V197 197 197 14V197 u = , Du = 197 %3D 197' 197

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Find the velocity and acceleration vectors of the particle whose position at time t seconds is given…

A: We have a given position vector of any particle. And we have to find velocity and acceleration…

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

A:

Q: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.