I'm looking if someone could take me out of a doubt I have with this problem.
Suppose temperature at a point $(x,y,z)$ in space is given by $T(x,y,z)=\frac{80}{1+x^2+2y^2+3z^2}$, where $T$ is measured in celsius and $x,y,z$ in meters. In what direction does the temperature increase more rapidly in relation to the point $P=(1,1,-2)?$
From what I know, a function $f$ changes more rapidly in a point $P$ in direction of it's gradient $\nabla f_{(P)}$ at that point, however, in the problem I'm asked in what direction the tempareture increase more rapidly, so this means that the direction of greater increase of temperature would be the negative of gradient of $T$ evaluated in $P$, am I right?
Thanks.