Absolute extrema of a function with two constraints

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This graph shows the constaint set \[g(x,y,z) = x^2+z^2-2 = 0 \quad \text{and} \quad h(x,y,z) = y - z = 0\] as a blue curve. The objective is to find the maximum and minimum of \[f(x,y,z) = -2x+3y-5z\] on the constraint set by looking at the level surface of \(f(x,y,z)\) which is shown as a red surface.

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Joseph Lo, Created with GeoGebra