12.(1999, AB-4) Suppose that the function fhas a continuous second derivative for all x, and that ( )02f( )03f′=−, and ( )00f′′=. Let gbe a function whose derivative is given by ( )( )( )()232xgxefxfx−′′=+for all x(a)Write an equation of the tangent line to the graph of fat the point where 0x=(b)Is there sufficient information to determine whether or not the graph of fhas a point of inflection when 0x=? Explain your answer. (c)Given that ( )04g=, write an equation of the line tangent to the graph of gat the point where 0x(d)Show that ( )( )( )( )()262xgxefxfxfx−′′′′′=−−+. Does ghave a local maximum at 0x=? Justify your answer. =, . . =.