45 mins ago, by
Tuki if i have gradient for function $f(x,y)$ $$ \nabla f(x,y)=\begin{bmatrix} \frac{\delta}{\delta x} \\ \frac{\delta}{\delta y} \end{bmatrix} $$ so for example vector $ \hat{a} =\nabla f(x_0,y_0)$ points to the direction of largest increase of function $f(x,y)$ at point $(x_0,y_0)$. Now if i want to find out the largest decrease in $f(x,y)$ we can call this vector $\hat{b}$ is it just $\hat{b}= -\nabla f(x_0,y_0) $ we make both components negative ? that would flip vector in negative direction ?