Is this question asking for us to find the saddle point,maximum,minimum?I'm confused,how would I go about doing this?
Suppose you are climbing a hill of height z whose shape is given by the equation z(x,y)=1000-0.01x^2-0.04y^2 and you are standing at the point with the coordinates(240,80,168).
In which direction is the line of greatest steepness? Give your answer as unit vector.
Use a directional derivative to find the rate of climb in this direction.
The directional derivative is:
f is your function, and v is the direction in which you are calculating the derivative.
The direction in which the line is steepest is when
Hence the directional derivative in that direction is:
So
1) Find in terms of x, y and z.
2) Plug in your point (240,80,168)
3) Find the magnitude of the vector you get.