Directional derivatives and gradients - Printable Version +- Southperry.net (https://www.southperry.net) +-- Forum: Social (https://www.southperry.net/forumdisplay.php?fid=14) +--- Forum: Rubik's Cube (https://www.southperry.net/forumdisplay.php?fid=58) +--- Thread: Directional derivatives and gradients (/showthread.php?tid=64442)

Directional derivatives and gradients - Imagine - 2013-05-20 If f(x, y, z)=3xy+z^2 and u is the unit vector in the direction of (0, -2, 2), then the directional derivative at the point (−4−1−4) in the direction of u (Duf(−4,−1, −4)) is? Duf(-4, -1, -4) = gradient of f at (-4, -1, -4) * (0, -2, 2) gradient of f = (3y, 3x, 2z) Plug in (-4, -1, -4) and get: (-3, -12, -8) Duf(-4, -1, -4) = (-3, -12, -8) * (0, -2, 2) = 0 + 24 - 16 = 8 This answer is wrong, and I have no idea what went wrong. Directional derivatives and gradients - Kalovale - 2013-05-21 Directional derivative denotes the rate of change of the function value when you take one unit-length step along the "directional" vector in parameter space. They gave you a vector u in the direction of the vector <0, -2, 2>, u itself is not <0, -2, 2>. In short: