Question

T(x,y,z) = 1/(1 + x^2 + y^2 + z^2)

where T is measured in degrees Celsius and x,y,z in meters. In which direction does the temperature increase fastest at the point (1,1,-2)? What is the maximum rate of increase?

Answer 1

I could a brief explanation of what to do, don't have to give a full explanation just get me started. Already found the gradient vector of T, plugged in the point, used my own directional vector u = <x,y,z> to get a new function F as a function of the derivative in any given direction, tried to maximize and failed. ended up with gradient(F) = <-1/22, -1/22, 1/11> What now?

Answer 2

For this information, you must give me your soul.

Answer 3

Hahaha. Seriously, I could use some help.

Answer 4

And you think I'm not serious?

Answer 5

Shows how much help you really need...

Answer 6

Directional derivatives require me to go back half a semester and look up notes from then.

Answer 7

Directional Derivative is just the dot product of the vector function and a directional vector.

Answer 8

Okay... And...
Doesn't help me at all/you don't know what I'm talking about.
Give me your soul if you want help or else start crying.

Answer 9

Cool story bro. Go troll someone else.

Answer 10

Take the magnitude of your gradient vector to find maximum rate of change, it seems like you already know what to do.