6) F(x) = (x-2)2/3

    F’(x) = (2/3) (x-2)-1/3

  

    F”(x) = (2/3)(-1/3)(x-2)-4/3

             = (-2/9)(x-2)-4/3

 

 

7) F(x) = (1-x)2 (1+x)3

   

    F’(x) = 3(1+x)2(1-x)2 – 2(1+x)3(1-x)

             = (1+x)2 [ 3(1-x)2 - 2(1+x)(1-x) ]

             = (1+x)2 [ 3(1-x)2 – 2(1-x2) ]

             = (1+x)2 [ 3(1-2x+x2) – 2 + 2x2 ]

             = (1+x)2 (3-6x+3x2-2+2x2)

             = (1+x)2 (5x2-6x+1)

 

   F”(x) = (1+x)2 (10x-6) + 2(5x2-6x+1)(1+x)

            =  (1+2x+x2)(10x-6) + 10x2-12x+2+10x3-12x2+2x

            = 20x3+12x2-12x-4

            = 4(5x3+3x2-3x-1)