Find the global max/min for z=xy^2 - 5 on the region bounded by y=x

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SUMMARY

The discussion focuses on finding the global maximum and minimum of the function z=xy^2 - 5 within the region defined by the curves y=x and y=1-x^2. A critical point was identified at (0,0), but the participants expressed uncertainty about how to evaluate this critical point in relation to the boundaries of the defined region. The analysis requires evaluating the function at the boundaries and comparing these values to the critical point to determine the global extrema.

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countzander
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Find the global max/min for z=xy^2 - 5 on the region bounded by y=x and y=1-x^2 in the xy-plane.
 
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And what have you done so far?
 


I found the critical point of z=xy^2 - 5 at (0,0), but I do not know how to relate this to the boundary.
 

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