Suppose that f(x) has a continuous first derivative for all x http://upload.wikimedia.org/math/7/b...e1a4c7cff0.png R

a) Prove that f(x) is concave if and only if f(x*)+(x-x*)f′(x*) ≥ f(x) for all x and x* http://upload.wikimedia.org/math/7/b...e1a4c7cff0.png R

b)Given that f(x) is concave, prove that x* is a global maximum of f(x) is and only if f′(x*)= 0

c) Given that f(x) is strictly concave, prove that it cannot possess more than one global maximum.

my understanding of graphs is very poor any help on this would be greatly appreciated.

Dave