I got the second one right.The temperature at a point (x,y,z) is given by , where is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector.

1) Find the rate of change of the temperature at the point (1, -1, 2) in the direction toward the point (-1, -5, 5).

2) In which direction (unit vector) does the temperature increase the fastest at (1, -1, 2)?

3)What is the maximum rate of increase of at (1, -1, 2)?

$\displaystyle <(-400e^{-49/36})/ \sqrt(e^{-98/36}{(-400)^2+(100)^2+(-800/9)^2}), $$\displaystyle 100e^{-49/36}/ \sqrt(e^{-98/36}{(-400)^2+(100)^2+(-800/9)^2}), $$\displaystyle -(800/9)e^{-49/36}/ \sqrt(e^{-98/36}{(-400)^2+(100)^2+(-800/9)^2})>

$

but I do not get 1 and 3.

I tried to do both and i have

1) 0

3) $\displaystyle \sqrt(e^{-98/36}{(-400)^2+(100)^2+(-800/9)^2})$

But both are not right and I am totally out of idea how to solve it. Please someone help me