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  3. consider the equation f(x,y) = −4x2+4x+y2+2y

Consider the equation f(x,y) = −4x2+4x+y2+2y, the picture shows some of it’s level curves. a. Completing the...

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Basic Math

Consider the equation f(x,y) = −4x2+4x+y2+2y, the picture showssome of it’s level curves.

a. Completing the square, write the equations and identify thetraces f(x,y) = k for k = −1,0.

.(b) Draw the direction of fastest increase at the point (1,1)

.(c) Find the rate of change of f (x, y) = z at (1, 1) in thedirection of 〈−1, −2〉.

.(d)   Find an equation for the tangent plane to thegraph of f at (1, 1, 3).

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