Let f(x,y,z) = .Find the directional derivative of f(x,y,z) at the point (1,3,-2) in the direction of the vector [3,-1,4]
So what is the function ?
by the way search for:
calculator-online.net/directional-derivative-calculator/
well, you know it's ∇f•[3,-1,4]
so plug and chug.
To find the directional derivative of the function f(x, y, z) at the point (1, 3, -2) in the direction of the vector [3, -1, 4], we need to follow these steps:
Step 1: Calculate the gradient of the function f(x, y, z).
The gradient of a function represents the vector of its partial derivatives with respect to each variable. In this case, we have:
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Step 2: Evaluate the gradient at the given point.
Substitute the coordinates of the point (1, 3, -2) into the partial derivatives to find:
∇f(1, 3, -2) = (∂f/∂x(1, 3, -2), ∂f/∂y(1, 3, -2), ∂f/∂z(1, 3, -2))
Step 3: Calculate the dot product of the gradient and the directional vector.
The directional derivative of f(x, y, z) in the direction of the vector [3, -1, 4] can be found using the dot product:
Df = ∇f(1, 3, -2) · [3, -1, 4]
Step 4: Simplify the expression to get the final result.
Evaluate the dot product to obtain the directional derivative at the given point.
Please note that the provided function f(x, y, z) is incomplete in your question. To find the directional derivative, we need a specific function that involves x, y, and z in order to calculate the partial derivatives and gradient.