Show that the approximate value of the American commodity put option based on the quadratic approximation method

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Show that the approximate value of the American commodity put option based on the quadratic approximation method is given by

P(S, T) = P(S, T)  S* 91 91 [1-eh-N(-d(S*))](/)S*.">

Explain why the formula holds for all values of b.

Show that 

and P(S, T) = P(S, T)+c KS,  as (S*, t) = e(br)t N(-d (S*)).

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