00:01
In this problem, we are given the equation of a surface for which we want to plot its level curves for at least five different levels.
00:08
So here we have our surface z written as a function of x and y.
00:15
When we want to plot the level curves, what we do is we set our variable c, z, excuse me, to some constant c.
00:28
So in this case, we have that f of x, y is equal to c.
00:35
And what's going to happen is it's going to in essence eliminate one variable, so our three -dimensional plot can now be plotted into two dimensions.
00:45
And in this specific case, our curve c, z, excuse me, is equal to x times y.
00:54
So in essence, we want to plot our curves in the form of y is equal to c over x, for c ranging between minus 2, minus 1, 0, 1, and 2.
01:13
So these are the five level curves we want to plot and they're all going to be inverse functions.
01:19
So let's sketch this graph.
01:29
Let's sketch our inverse function for when c is equal to 1.
01:36
So we know what this looks like.
01:40
An inverse function looks like this and like this.
01:49
So in red are the level curves for c equal to 1.
01:55
And red and solid curve.
01:57
So now i'm going to draw a dotted curve for when c is equal to 2.
02:00
So when c is equal to 2, we also have an inverse curve, but a shift multiplied by a constant, which is going to just increase our curve.
02:12
Something like this...