1. ## Directional Derivative Question

In what direction does the directional derivative for f(x, y) = x2y at (1, 1) have

A. Value 1?

B. Value -2?

C. Is there a direction for which the value is 4?

I'll be completely honest, I don't even know where to begin on this question, I have never seen a problem like it before therefore I come to you guys lost and looking for help, anything will be appreciated.

2. The gradient is $\bigtriangledown f (x,y)= (2y, 2x)$, and at $(1,1)$ we have $\bigtriangledown f (1,1)= (2, 2)$. The directional derivative in the direction of the unit vector $u=(a,b)$ is $\bigtriangledown f (1,1) \cdot (a,b)=2a+2b$. So if you know that this directional derivative is equal to some value $X$, you want to solve the system of equations:

$2a+2b=X$

$a^2+b^2=1$

for $a,b$.

3. I copy pasted wrong, it is supposed to be f(x,y)=(x^2)y, however, i see the process is the same, so after getting the directional derivative, i set it equal to some value, however, where did the a^2 + b^2 = 1 come from?

4. Originally Posted by Bruno J.
...The directional derivative in the direction of the unit vector $u=(a,b)$ ...