Find the absolute maximum and minimum values of f(x, y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.

The absolute maximum and minimum is

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

The only solution to this system of equations is the point (0, 4), which lies in the domain.

is a saddle point.

Boundary points -  

Along boundary  

Values of f(x) at these points.

Therefore, the absolute maximum and minimum is

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