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Answer 1 · 2017-04-30T22:26:20

(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)

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