Consider the following function f: R² → R [1 2] 47 21 f(x) = x¹ T x+x™ +6. (a) Find the gradient and Hessian of f at the point [1,1]. (b) Find the directional derivative of f at [1,1] with respect to a unit vector in the direction of maximal rate of increase. (c) Find a point that satisfies the FONC (interior case) for f. Does this point satisfy the SONC for a minimizer?

Q: 4. (a) Determine the directional derivative of f(x, y, z) = zety at the point (1, −1, 1) in the…

A:

Q: Find the directional derivative of f(x, y) = x²y³ in at the point (−1, −1) in the direction û given…

A:

Q: Determine the directional derivative of f(x, y, z) = tan-1 221) where U = (-1,2,2) at P(0, 1, 1).…

A: The given function is fx,y,z=tan-1xy22z2-1. The direction vector is u=-1,2,2 and the point is…

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

A:

Q: 4) Let f(x, y) = x² – 2xy a) Find the gradient of f at the point (1, –2). b) Use the result of (a)…

A:

Q: Example: Find the directional derivative of f(x, y, z)=x²-yz+xz² at P(1,-4, 3) in the direction from…

A: Directional derivative of f(x,y,z) in direction of some vector a is given by , Directional…

Q: Find the directional derivative of f(x, y) = x²y³ + 2x¹y at the point (-3, -1) in the direction = =…

A: