Question

Rate of greatest increase

Answer 1

for f(x, y, z) = (−3x − 3xy + 12y + 4z)e^(−xy) i just have to take its derivative and for 'at the point (x, y, z) = (0, 1, −9)', i just plug these numbers in?

Answer 2

yup i think so

Answer 3

i derive wrt what though? x, y, z and then i add the three up?

Answer 4

I think we need to start off finding the gradient of f
\[\nabla f =<\frac{\partial f}{\partial x}, \frac{ \partial f}{\partial y}, \frac{\partial f}{\partial z}>\]

Answer 5

Also was that point given?

Answer 6

are we just looking for the direction of greatest increase at the point given (if that is the point that given )

Answer 7

if so the next step is just to evaluate the gradient there at the point given

Answer 8

we are looking for the rate of greatest increase at that given point, so i plug the numbers in the differentials and add them up?