Answers>Maths>A Level>Article

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 y = 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)

Answered by Abi I. • Maths tutor

11121 Views

See similar Maths A Level tutors

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

Related Maths A Level answers

Find the coordinate of the stationary point on the curve y = 2x^2 + 4x - 5.

find dy/dx for the equation y = 6x ^(1/2)+x+3

Given y = 2sin(θ) and x = 3cos(θ) find dy/dx.

Solve dy/dx= (x√(x^2+3))/e^2y given that y=0 when x=1, giving your answer in the form y = f(x)