Given y = 2x(x2 – 1)5, show that (a) dy/dx = g(x)(x2 – 1)4 where g(x) is a function to be determined. (b) Hence find the set of values of x for which dy/dx > 0

Given = 2x(x2 – 1)5, show that
(a) dy/dx = g(x)(x2 – 1)4 where g(x) is a function to be determined.

dy/dx= (2)(x2 – 1)5 + (2x)*5(x2– 1)4(2x)

dy/dx= (x2 – 1)4( 2(x2 – 1) + 20x2 )

g(x) = 2(x2 – 1) + 20x2

(b) Hence find the set of values of x for which dy/dx > 0
(x2 – 1)4( 2(x2 – 1) + 20x2 ) = 0

2(x2 – 1) + 20x2 = 0

22x2 - 2 = 0
2(11x2 - 1) = 0

11x2 = 1

x = +-√(1/11)

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