By about how much will f(x, y,z) = In root x^2 +y^2 +z^2 change if the point P(x, y, z) moves from P0(2,2,6) a distance of ds = .1 units in the direction of 3i+6j-2k?

Step-by-step explanation:

In order to find the answer we need to calculate the directional derivative:

The gradient of f is:

The unit vector can be found as:

The directional derivative at the point is:

Finally, the problem tell us that the point moves a distance of 0.1 units. Hence f(x,y,z) will move:

i believe the correct answer is b.