Find the stationary points of y=x^3 + 3x^2 - 9x - 4

The stationary points of the function are the points at which the gradient is equal to 0. (If you draw out a standard y=x^3 graph, you can see the gradient is 0 at the points where the graph changes direction)1) Differentiate the expression to find the gradient2) Set this differential equation to equal 0, as this will give you the points at which the gradient is equal to 03) Find the roots of the equation by factorizing4) Substitute each of the roots found in place of 'x' in to the original equation for the graph, to find the corresponding y values.

NB
Answered by Nikhita B. Further Mathematics tutor

2665 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

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]


How do you use derivatives to categorise stationary points?


How can I find the equation of a straight line on a graph?


Find the coordinates of the minimum/maximum of the curve: Y = 8X - 2X^2 - 9, and determine whether it is a maximum or a minimum.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning