Question

If function f(x,y,z)=2xy−z²what is the gradient of f at point (x,y,z)=(3,−1,1) ?

Answer 1

The gradient of the function f(x,y,z)=2xy−z² at point (3, -1, 1) can be calculated by finding the partial derivatives of the function with respect to x, y, and z at that specific point. The gradient at (3, -1, 1) is (-2, 6, -2).

Step-by-step explanation:

The gradient of a function is a vector field that points in the direction of the greatest rate of increase of the function, and whose magnitude is the greatest rate of change of the function.

The gradient of function f(x,y,z)=2xy−z² is denoted by ∇f or grad f. It's calculated as follows: