# Thread: Multivariable Caculus Leverl Curves

1. ## Multivariable Caculus Leverl Curves

Am studying for my final exam lol, this question is confusing me as well,

the equation give is f(x,y)=x^2/4 + y^2/9

(a) Sketch at least three labeled level curves of f and the gradient vector at a point on each of them.

Kay I know how to draw the level curves i set f(x,y)=z say , z constant i get an ellipse but how do I draw the gradient vectos at each point? as they say from reading from my textbook it says its orthogonal to the level curves so i just draw perpendicular lines to the points on the level curves.

(b) Find an equation to the tangent plane, at f(2,3) thats just using the the partial dervitives of fx and fy i think

2. For your gradient vectors --yes they are orthognal to the curves but
in the direction of increasing z --so on one level curve the gradient is in the direction of a level curve of greater z value

For your second question yes

z = fx(2,3)*(x-2) +fy(2,3)*(y-3) + f(2,3)

3. What do you mean exactly by the same level as increasing z value I quite get what you say! thank!

4. if you have a level curve where say z = 1 and one where z = 2 then the gradient on the level curve z= 1 is orthogonal and points toward the level curve where z = 2

5. Kay gotcha am gonna work on that graph now thanks! dude!