Notice that all of the vertical traces are parabolas, Mathematics

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Notice that all of the vertical traces are parabolas

Consider Figure below. You will notice that this Hyperbolic Paraboloid has the equation z = (x/2)² - (y/3)² = (x²/4) - (y²/9). For simplicity we give this function the name f(x, y) so that f(x,y) = (x²/4) - (y²/9).

1790_The Hyperbolic Paraboloid.png

a. Notice that all of the vertical traces are parabolas whether these vertical traces are in the planes x = a or in the planes y = b, where a and b can be any real numbers. Which of these vertical traces are parabolas opening up and which are parabolas opening down?

b. Is f_xx positive or negative?

c. Is f_yy positive or negative?

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Mathematics: Notice that all of the vertical traces are parabolas

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