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Bordered Hessian element The Lagrangian is L=ln(x+y^2) -z^3/(3*y) -x*y +λ*(x*z +3*x^2*y -r), where r is a...

Bordered Hessian element

The Lagrangian is L=ln(x+y^2) -z^3/(3*y) -x*y +λ*(x*z +3*x^2*y -r), where r is a parameter (a known real number). Here, ln denotes the natural logarithm, ^ power, * multiplication, / division, + addition, - subtraction. The border is at the top and left of the Hessian. The variables are ordered λ,x,y,z.

Find the last element in the second row of the bordered Hessian at the point (λ,x,y,z) =(0.11, 0, 2440, 0.01167). This point need not be stationary and you do not have to solve first order conditions to calculate the bordered Hessian. Write the element as a number in decimal notation with at least two digits after the decimal point. No fractions, spaces or other symbols.

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