Find the stationary points and their nature of the curve y = 3x^3 - 7x + 2x^-1

To start, we need to know that the gradient of the curve at the stationary points is 0 and that when the second derivative is less than 0, there is a maximum and when the derivative is greater than 0, there is a minimum. In order to find the gradient of the curve, we differentiate y. This gives dy/dx = 9x2 - 7 - 2x-2.We know that at the stationary points, dy/dx = 0. Hence, 9x2 - 7 - 2x-2 = 0 and x = 1, -1. To find the nature of these points, we need to differentiate one more time and substitute the values of x into the second derivative. d2y/dx2= 18x + 4x-3.For x = 1, d2y/dx2= 22. Therefore at x = 1, there is a minimum.For x = -1, d2y/dx2= -22. Therefore at x = -1, there is a maximum.

AA
Answered by Arjun A. Maths tutor

4095 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I integrate ∫ xcos^2(x) dx ?


What are the rules for decomposition of partial fractions?


Find the derivative of A^4 + 2A^2 - 3A + 4


A straight line passes through the point (2,1) and has a gradient of 3. Find the co-ordinates of the points where this line intersects the axes


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences