The problem involves finding the rate of change of the function f(x, y, z) = 3x + 2y + 4z at the point (1, 2, 3) constrained to the plane y = 2. The discussion centers around the implications of this constraint and how it affects the derivatives involved.
The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the use of gradients to find the rate of change, but there is no explicit consensus on the best approach or the implications of the definitions being discussed.
Participants question the clarity of the problem statement and whether it was well-written. There is also a discussion about the nature of the gradient and its relationship to the rate of change in multiple dimensions.
mfb said:
This is possible, right.
No, this is not "bad written" (or even "badly written"supermiedos said:
). Since you are asked about its rate on change on y= 2, replace y by 2: f(x, z)= 3x+ 4+ 4z. The rate of change of that, at (1, 2, 3) is the length of the gradient vector evaluated at (1, 2, 3). (If the function really is what you wrote without any powers, its gradient vector is a constant and the point (1, 2, 3) is irrelevant.)HallsofIvy said:No, this is not "bad written" (or even "badly written"
This is always zero with 2 or more variables, if the function is differentiable.supermiedos said:
Right