4.7

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4.7

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The surface of a mountain is modeled by the graph of the function z = 2xy - 2x² - y² - 4x + 6y - 8, where z is the height in kilometers. If sea level is the xy-plane, how high h is the mountain above sea level? (Use symbolic notation and fractions where needed.) height: km

Find the absolute maximum and absolute minimum of the function z = f(x, y) = 14x² − 56x + 14y² - 56y on the domain D:x² + y² ≤ 81. (Use symbolic notation and fractions where needed.) absolute min: absolute max:

Find the local maxima, local minima, and saddle points, if any, for the function 15x + 5y (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *, *), (*, *, *)... Enter DNE if the point does not exist.) local min: local max: saddle point:

Find the local maxima, local minima, and saddle points, if any, for the function z = 3x³ – 36xy − 3y³. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *, *), (*, *, *) ... Enter DNE if the points do not exist.) local min: local max: saddle points:

Find the local maxima, local minima, and saddle points, if any, for the function z = = 4x³ - 60xy + 4y³. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *, *), (*, *, *) ... Enter DNE if the points do not exist.) local min: local max: saddle points: