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Section 6 Wrap Up Questions

  1. Explain why the derivative cannot be used to find global minima and maxima subject to a constraint.

  2. Are the following statements true or false? Give reasons for your answers. Assume the constraint \(g(x,y)=c\) is bounded and \(g\) is continuous.

    1. A function \(f(x,y)\) subject to the constraint always has a global minimum and a global maximum.
    2. A function \(f(x,y)\) subject to the constraint can have a global maximum at more than one point on its constraint.
    3. If the global minimum and global maximum of a function \(f(x,y)\) subject to the constraint are equal, then the function \(f(x,y)\) must be a constant function.
    4. If the global minimum and global maximum of a function \(f(x,y)\) subject to the constraint are equal, then the constraint coincides with a contour of \(f(x,y)\text{.}\)
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