# Directional Derivatives

1. May 23, 2014

### cooev769

I've come across a question which as really stumped me because I thought I knew how to do this but apparently not.

The question is that we have a tangent vector to a level curve of a function of two variables f(x,y) at a point P is (2,1). Hence by my logic this means grad of f x unit vector of (2,1) is 0. The next part is that the directional derivative of f at P in the direction (3/5, 2/5) is 1/5. Hence by applying the same operation above. Find the gradient of f at P. I would just evaluate both and use simultaneous equations. But the answer they arrive at is really nice at (1, -2) I can't get it myself. Any help would be appreciated thanks.

2. May 23, 2014

### Simon Bridge

Looks like the method I'd use. Please show your working - step by step.
Double check the algebra and arithmetic.