# Finding the Direction of a Function

1. Oct 23, 2011

### Ki-nana18

1. The problem statement, all variables and given/known data
Find the direction in which the function f(x,y)=x^2+sin(4y) increses most rapidly at the point P0=(1,0). Then find the derivative of f in this direction.

2. Relevant equations

3. The attempt at a solution
I think I have to find the gradient at point P0 and then find a unit vector is this right?

2. Oct 23, 2011

### SammyS

Staff Emeritus
Yes, for the first part of your question.

3. Oct 23, 2011

### Ki-nana18

Okay, I found the gradient <2x+sin(4y), x^2+4cos(4y)> and at point P0 it is
<2,5>. Now if I only have one point how do I find the unit vector wouldn't I need another point or an initial vector?

4. Oct 23, 2011

### LCKurtz

What do you need the unit vector for?

5. Oct 23, 2011

### Ki-nana18

Sorry. $\nabla$f=<2x, 4 cos(4y)>. Does the gradient at P0 tell me the direction in which the function increases most rapidly?

6. Oct 23, 2011

### LCKurtz

Yes, and there's more. What does the magnitude of the gradient represent?

7. Oct 24, 2011

### Ki-nana18

How fast the function increases?

8. Oct 24, 2011

### HallsofIvy

Staff Emeritus
In what direction? A function of several variables may have different rates of increase in different directions.