The directional derivative of a given function $w = f (x, y)$ at point $Po (1, 2) $in the direction toward $P1 (2, 3)$ is $2\sqrt2$ and in the direction toward $P2 (1, 0)$ is $(-3)$. What is the value of$\frac{dw}{ds}$ at Po in the direction toward the origin?
I don't understand what the question wants and how to solve, but I know that the topic is "Directional Derivative" so it contains partial derivatives and vectors, please tell me some tips and hints, where should I start?
If the function $f(x,y)$ is differentiable at x,y, then the directional derivative along a vector $\vec{v}$ can be found using $$ \nabla_{\vec{v}} f(x,y) = \vec{\nabla} f(x,y) \cdot \vec{v}. $$ The vectors $\vec{v}$ you can find using the given points. You also know the values of two of these directional derivatives. This should allow you to find the components of the vector $\vec{\nabla} f(x,y) = (a,b), \quad \forall a,b \in \mathbb{R} $.
I hope this helps.