Suppose the Graph Below Gives a Solution to the Differential $\frac { \mathrm { dP } } { \mathrm { ds } }$

Multiple Choice

Suppose the graph below gives a solution to the differential equation $\frac { \mathrm { dP } } { \mathrm { ds } }$ = g(P) where P is the price of a product and s is the weekly sales. Which of the following statements is/are true?
(I) g(M) = 0
(II) $g ^ { \prime } ( M ) = 0$
(III) $g \left( \frac { \mathrm { M } } { 2 } \right) _ { = 0 }$
(IV) g( $\mathrm { P } _ { 0 }$ ) > 0

A) I only
B) IV only
C) I, III, and IV
D) I and IV
E) I, II, and IV