A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.

We know that a stationary point is found when the gradient of the curve is equal to zero, this is found by equaling the derivative (dy/dx) equal to zero. Differentiating the expression will find a quadratic that can be factorised into two brackets, the two brackets represent the two co-ordinates of the two stationary points, one of which will be P=-2 and the other is found to be x=5/3.The second derivative of the expression can be found, and when P is substituted in, a value is found which represents if it is a maximum or minimum value of the curve. This is found to be d2y/dx2 = 22, which is a positive value and therefore a minimum curve point.

GS
Answered by Georgia S. Maths tutor

2932 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the inequality 􏰂|2x + 1|􏰂 < 3|􏰂x − 2|􏰂.


How would you differentiate the term 3x^3-2x^2+x-10


Express 4 sin(x) – 8 cos(x) in the form R sin(x-a), where R and a are constants, R >0 and 0< a< π/2


y=4x^3+6x+3 so find dy/dx and d^2y/dx^2


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