Question

Let f(x, y, z) = yz^2 + z√(1 + x). (a) Find the gradient of f at the point P(3, 2, 1).

Answer 1

To find the gradient of f at the point P(3, 2, 1), evaluate the partial derivatives with respect to each variable and evaluate them at the given point. The gradient vector is [0, 5, 5.5].

Step-by-step explanation:

To find the gradient of f at the point P(3, 2, 1), we need to find the partial derivatives of f with respect to each variable and evaluate them at the point P. The gradient of f is a vector that contains the partial derivatives.

The partial derivative with respect to x is 0, the partial derivative with respect to y is z^2, and the partial derivative with respect to z is 2yz + (√(1 + x))/2z. Evaluating these at P(3, 2, 1), we get the gradient vector [0, 5, 5.5].