Find the turning points on the curve with the equation y=x^4-12x^2

y = x^4 - 12x^2
dy/dx = 4x^3 - 24x
The turning points are where dy/dx = 0
4x^3 - 24x =0
x(4x^2 - 24) = 0 Therefore one of the turning points is at x = 0
4x^2 - 24 = 0
4x^2 = 24
x^2 = 6
x = +/- √6
Substitute the x coordinates back into the original equation to find y
The final coordinates are (0,0), (√6,-36) and (-√6,-36)

Answered by Maths tutor

4506 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate 2x^5 - 1/4x^3 - 5


How do you resolve forces on an object on an angled plane?


y=20x-x^2-2x^3. Curve has a stationary point at the point M where x=-2. Find the x coordinate of the other stationary point of the curve and the value of the second derivative of both of these point, hence determining their nature.


Suppose that you go to a party where everyone knows at least one other person, you get a bit bored and wonder whether there are at least two people which know the same number of people there.


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:

© 2025 by IXL Learning