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)