The appropriate option for the statement “If ( a , b ) is a critical point of f ( x , y ) , all second derivatives of f are continuous, and f x x ( a , b ) = 10 , f y y ( a , b ) = 3 , f x y ( a , b ) = 5 , then ( a , b ) is a:” from the given options ( a ) - ( d ) .

Question

The graph of the function f in the figure below consists of line segments and a semicircle. Let g be the function given by x 9(x) = * f(t)dt. Determine all values of r, if any, where g has a relative minimum on the open interval (-9, 9). y 8 7 6 5 4 32 1 Graph of f x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 678 -7 -8

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Chapter 14.7, Problem 2PT

To determine

The appropriate option for the statement “If (a,b) is a critical point of f(x,y), all second derivatives of f are continuous, and fxx(a,b)=10,fyy(a,b)=3,fxy(a,b)=5, then (a,b) is a:” from the given options (a)-(d).

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