Thread: 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)

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: $\displaystyle D_u f = \nabla f \cdot u$

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