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

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

a. Completing the square, write the equations and identify the traces 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 the direction of 〈−1, −2〉.

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

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Expert Solution

milcah answered 2 years ago
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