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

2235 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

How would you differentiate x^x?


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.


l1 and l2 are tangents of a circle. l1 intersects the circle at (3-√3,5) with a gradient of √3, and l2 intersects the circle at (3+√2,4+√2) with a gradient of -1. Find the centre of the circle, and hence find the radius of the circle.


How do I determine if a stationary point on a curve is the maximum or minimum?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences