Final answer:
The directional derivative of a function f at a point is found by computing the gradient of f at that point, which is composed of the partial derivatives with respect to each variable evaluated at the given point.
Step-by-step explanation:
To find the directional derivative of a function f, the first step is to compute the gradient of f at the given point. The gradient is a vector that consists of the partial derivatives of the function with respect to each of its variables. In the case of a function of three variables, f(x, y, z), the gradient at the point (1, 4, 2) is given by the vector of partial derivatives evaluated at that point:
grad(f) = ∇f = < ∂f/∂x, ∂f/∂y, ∂f/∂z > |_(1,4,2)
Without the specific function f, we cannot determine the exact partial derivatives. However, in general, to calculate them, you would take the derivative of f with respect to x, keeping y and z constant, then with respect to y, keeping x and z constant, and finally with respect to z, keeping x and y constant. These derivatives are then evaluated at the point (1, 4, 2).