How is the derivative of a differentiate function f(x, y, z) at a point P_0 in t
ID: 2877179 • Letter: H
Question
How is the derivative of a differentiate function f(x, y, z) at a point P_0 in the direction of a unit vector u related to the scalar component of (nabla f)p_0 in the direction of u? Give reasons for your answer. Choose the correct answer below. A. The directional derivative is the scalar component. Since nabla f middot u = (nabla f)_p_0 middot u. B. The directional derivative is a twice the scalar component. Since nabla f is evaluated at P_0, the scalar component of nabla f in the direction of u is nabla f middot u = (nabla f)p_0 middot u = 2 middot (nabla f)p_0 C. The directional derivative has no relation to the scalar component Since (nabla f)p_0 = P_1 i + P_2 j, the resulting vector has no relation to (nabla f)p middot in the direction of u. D. The directional derivative is the opposite of the scalar component. Since nabla f is evaluated at P_0, the scalar component of nabla f in the direction of u is nabla f middot u = - (nabla f)p_0 middot u.Explanation / Answer
Option A is correct since the directional derivative is a scalar component and it is defined as the dot product of grad f and unit vector.