A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.

dy/dx = 9x^2 + 2ax + b

x = 2, dy/dx = 9(2)^2 + 2a(2) + b = 36 + 4a + b

x = 1, dy/dx = 9(1)^2 + 2a(1) + b = 9 + 2a + b

36 + 4a + b = 2(9 + 2a + b)

b = 18

x = -1, dy/dx = 0 = 9(-1)^2 + 2a(-1) + 18

9 - 2a + 18 = 0

a = 13.5

AR
Answered by Alistair R. Further Mathematics tutor

2104 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

A straight line passes trough the points A(-4;7); B(6;-5); C(8;t). Use an algebraic method to work out the value of t.


y=(6x^9 +x^8)/(2x^4), work out the value of d^2y/dx^2 when x=0.5


Differentiate y = x*cos(2x)


f(x) = 3x^3 – x^2 – 20x – 12 (a) Use the factor theorem to show that (3x + 2) is a factor of f(x). [2 marks] (b) Factorise f(x) fully. [3 marks]


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