- #1
jegues
- 1,097
- 3
Homework Statement
Find the rate of change of the function,
[tex]f(x,y,z) = cos(\pi x y) + xln(z^{2}+1),[/tex]
with respect to length [tex]s[/tex] along the curve,
[tex]y=-3x, z=x^{2}-y^{2}+9,[/tex]
directed so that x increases, at the point (-1,3,1).
Homework Equations
The Attempt at a Solution
See figure attached.
I wrote parametric equations for the curve, and threw them into a vector.
Since at the point (-1,3,1) t=-1, I evaluated the vector accordingly.
The question says "so that x increase" so I reversed the direction of the vector by multiplying it by negative 1.
After this I found a unit vector that points in the same direction as the vector described previously.
Then I found the gradient of f and evaluated it at the point (-1,3,1).
After this I dotted the two to get the rate of change of f in the desired direction.
The solution lists the answer as,
[tex]\frac{ln(2) - 16}{\sqrt{266}}[/tex]
Where did I go wrong?