Answer :

max. value is 139 at x = 2 and min. value is 89 at x = 3

F(x)=6x2-24=0


6(x2-4)=0


6(x2-22)=0


6(x-2)(x+2)=0


X=2,-2


Now, we shall evaluate the value of f at these points and the end points


F(2)=2(2)3-24(2)+107=75


F(-2)=2(-2)3-24(-2)+107=139


F(-3)=2(-3)3-24(-3)+107=125


F(3)=2(3)3-24(3)+107=89


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