Directional Derivatives With Respect to Negative Vectors

Question

I understand this is probably a silly question but I'm with it struggling nonetheless. Consider the directional derivative of $f(x)=x^2$ at $x=1$ with respect to $u=-1$. I can see that this is equal to $-2$ but I struggle to relate this result with my notion of derivatives as slopes of tangent lines. Could someone explain, in elementary terms, how one should picture this result?

Answer 1

If you have the direction $u = -1$, you have to look to the left, usually, you look to the right. So you could just flip your function...

And if you sit at $x = 1$, and go to the left, the function goes downwards, so the slope is negative.