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I need to

minimize {- f (x) | a <=x <= b}

where f ( x) is a concave and twice differentiable function. In addition, a and b are

positive constants such that a <b. Assume that -f (x) exists in the given interval [a, b] .

Show that

if the optimal solution is at x*= a , then delta f (a) < 0 must hold and

if the optimal solution is at x*= b * , then delta f (b) > 0 must hold.

Any help is much appreciated