A curve has equation y = 20x −x2 −2x3 . (A) Find the x-coordinates of the stationary points of the curve.

Firstly, differentiate the equation to find dy/dx.
dy/dx = 20 - 2x - 6x2
As dy/dx represents the gradient, we know that for a stationary point the gradient must be zero, hence for the stationary points, we set dy/dx = 0.
dy/dx = 20 - 2x - 6x2 = 0
Now, we have a quadratic equation, which we can now put into brackets to find our solutions.
dy/dx = 0 = 6x2 - 2x +20 = (x+2)(6x-10)
From these brackets, we know if one set were to be zero, dy/dx would be zero and we will find our x coordinates for our stationary points.
If (x+2) = 0, then x=-2
Or, if (6x-10) = 0, then x=10/6 = 5/3 simplified

BW
Answered by Bradley W. Maths tutor

5520 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is 'completing the square' and how can I use it to find the minimum point of a quadratic curve?


Given that y=4x^3-(5/x^2) what is dy/dx in it's simplest form?


Prove or disprove the following statement: ‘No cube of an integer has 2 as its units digit.’


Find the first derivative of y=2^x


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