g(x)= f(x)+f′(x)= ax？ +x？ +bx+3ax？ +2x+b =ax？ +(3a+ 1)x？ +(2+b)x+b

G(x)= odd function.

g(-x)=-g(x)

therefore

b=0

3a+ 1=0

a=- 1/3

therefore

f(x)=- 1/3x？ +x？

g(x)==ax？ +(3a+ 1)x？ +(2+b)x+b

=- 1/3x？ +2 times

g( 1)=- 1/3+2=5/3

g(2)=-8/3+4=4/3

The derivative of g(x) =-x? +2=0

X= radical number 2= 1.4

X=- root number 2=- 1.4 (deleted)

g( 1.4)=- 1/3( 1.4)？ +2( 1.4)= 1.9

(Calculated by root number 2 is 2/3 of root number 4)

So the maximum value is g( 1.4)= 1.9.

(Calculated by root number 2 is 2/3 of root number 4)

The minimum value is g(2)=4/3.