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

2117 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

GCSE or A-level Maths: How can I find the x and y intercepts of a cubic function?


Work out the gradient of the curve y=x^3(x-3) at the point (3,17)


In a chess club there are x boys and y girls. If ten more boys join and one more girl joins, there is an equal amount of boys and girls. Knowing that y = 2x+2, Calculate x and y. [4 marks]


Solving equations with unknown in both sides


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