Question

Question #7f620

Answer 1

(a)

`nabla f_{(-1,2)} = <2x - y, -x + 2y>_{(-1,2)} = <-4,5>`

(b)

We can do this many ways. But if we agree in differential terms that for a level curve:

`color(red)(df) = f_y dy +f_x dx color(red)(= 0)`

Then:

`dy/dx = - (f_x)/(f_y)`, the implicit function theorem

And this means that:

`dy/dx = - (2x-y)/(- x + 2y) = (4)/(5)`

So we say that:

`y = m x + c = 4/5 x + c`

And we plug in a value, `(-1,2)`, so that: `y = 2/5 ( 2 x + 7)`

(c)