Find the maximum rate of change of f at the given point and the direction in which it occurs.

Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(x, y, z) = (8x + 4y)/z, (20, 8, -4)
So I got <-2,-1,-12> But I got it wrong!

f(x,y,z) = (8x + 4y) / z = 8x/z + 4y/z

Find gradient:
∇f = < ∂f/∂x, ∂f/∂y, ∂f/∂z >
∇f = < 8/z, 4/z, -(8x+4y)/z² >

∇f(20, 8, -4) = < 8/-4, 4/-4, -(160+32)/16 > = < -2, -1, -12 >

Maximum rate of change = √(4+1+144) = √149
in direction < -2, -1, -12 >

I get same direction.
Did you get the same rate of change?
Perhaps this is where you have a problem.

Ματπmφm