which of these is not a critical point of the given function subject to the indicated constraint: constraint
is it (0,1) or or (1,0)
what i don't understand is how to approach this problem, thanks.
Notice that the third pair doen't even satisfy the constraint. Nonetheless,
... is by visualising, for sure.
Online 3-D Function Grapher
... and try to see the constraint as selecting just points on that surface (z = ...) that intersect with the plane (y = -1/2 x + 1) which is the plane passing vertically through the line y = -1/2 x + 1.
Then imagine getting the projection of that intersection against the x-z plane, where it will trace a curve which is z = just the result of replacing y with -1/2 x + 1. Sketch this curve, and locate the other two points to see that they are indeed critical.
PS: this problem may be for introducing you to Lagrange multipliers. Do the above first, though, and then plugging in the two equations as f and g here, Lagrange multiplier - Wikipedia, the free encyclopedia should make good sense.