Rate of Change as moving toward a point

• March 4th 2008, 03:43 PM
crwhd4
Rate of Change as moving toward a point
Find the rate of change of f(x,y,z) = ln(x+yz^2)-sin(y+z)+xe^y at the point (0,1,-1) as you move toward the point (4,1,2)
• March 4th 2008, 04:43 PM
Jhevon
Quote:

Originally Posted by crwhd4
Find the rate of change of f(x,y,z) = ln(x+yz^2)-sin(y+z)+xe^y at the point (0,1,-1) as you move toward the point (4,1,2)

you want the directional derivative here.

first, find the vector from (0,1,-1) to (4,1,2).

then find the unit vector in that direction

then use the formula: $D_u f = \nabla f \cdot u$

where $\nabla f$ is the gradient vector of $f$ (at the point (0,1,-1)), $\cdot$ is the dot product and $u$ is the unit vector i asked you to find.