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)

AI
Answered by Abi I. Maths tutor

9306 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I sketch a graph of a polynomial function?


Why do you not add the 'plus c' when finding the area under a graph using integration even though you add it when normally integrating?


A quantity N is increasing with respect to time, t. It is increasing in such a way that N = ae^(bt) where a and b are constants. Given when t = 0, N = 20, and t = 8, N = 60, find the value: of a and b, and of dN/dt when t = 12


Express (3 + 13x - 6x^2)/(2x-3) in the form Ax + B + C/(2x - 3)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences