Find the directional derivative of f(x,y,z)=3xy+z^2 at the point (−2,−2,2) in the direction of the maximum rat?

May 2021 2 147 Report

Find the directional derivative of f(x,y,z)=3xy+z^2 at the point (−2,−2,2) in the direction of the maximum rat?

Find the directional derivative of f(x,y,z)=3xy+z^2 at the point (−2,−2,2) in the direction of the maximum rate of change of f.

f_u(−2,−2,2)=D_uf(−2,−2,2) =?

The directional derivative in the direction of maximum change is simply the

magnitude of the gradient vector at the given point.

Now grad(f) = < 3y, 3x, 2z >, which at (-2,-2,2) is <-6, -6, 4>.

The magnitude is sqrt(6^2 + 6^2 + 4^2) = sqrt(88) = 2*sqrt(22).