The contour diagram of a function z=f(x,y) is given below. Determine the sign of the second...

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The contour diagram of a function z=f(x,y) is given below. Determine the sign of the second partial derivatives at the point P. Note the contours below all have negative values. 3.5 3 2.5 -8- 9 ---8- 2 1.5 1 0.5 9 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 fxx fxy fyy 1. Positive 2. Negative 3. Zero The contour diagram of a function z=f(x,y) is given below. Determine the sign of the second partial derivatives at the point P. Note the contours below all have negative values. 3.5 3 2.5 -8- 9 ---8- 2 1.5 1 0.5 9 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 fxx fxy fyy 1. Positive 2. Negative 3. Zero

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A nice problem in multivariable calculus To determine the sign of the second partial derivatives at the point P well analyze the contour diagram and identify the behavior of the function near the point Point P 2 15 From the contour diagram we can see that 1 The contours are curved and do not change direction abruptly near the point P This suggests that the second partial derivatives are not discontinuous or zero at this point 2 The contours are concave upward near the point P indicating that the function is increasing in both x and y directions This suggests that the second partial derivatives are positive Therefore we can conclude that fxx partial derivative ... View the full answer