A curve has equation y = 20x - x^2 - 2x^3 . The curve has a stationary point at the point M where x = −2. Find the x- coordinate of the other stationary point of the curve

A stationary point on a curve is when the differential of the equation of the curve = 0. In other words when dy/dx = 0Take the equation in the question: y = 20x - x2 - 2x3A simple rule to find the differential of the curve is to multiply that power by the value and drop that power by one. e.g. the differential of 2x3: dy/dx = 6x2.Therefore, dy/dx = 20 - 2x - 6x2.As the stationary point is when dy/dx = 0. Therefore, 20 - 2x - 6x2 = 0.factorise this quadratic. (x + 2 )(-6x + 10) = 0Therefore, the other stationary point is x = 10/6 which can be simplified to x = 5/3

HJ
Answered by Henry J. Maths tutor

3888 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C is defined by x^3 – (4x^2 )y = 2y^3 – 3x – 2. Find the value of dy/dx at the point (3, 1).


Find the equation of the tangent to the curve y=x^3 + 4x^2 - 2x - 3 where x = -4


Find the stationary point of y=3x^2-12x+29 and classify it as a maximum/minimum


Given that x = cot y, show that dy/dx = -1/(1+x^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