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.

Differentiate to get dy/dx=20-2x-6x^2Then stationary points occur when dy/dx = 0 so 0 = 20-2x-6x^2 Factorise to get x= -2, x=5/3Differentiate dy/dx to get second derivative = -2-12x at x=5/3 is -22 so max pointat x=-2 second derivative is 24>0 so min point.

EJ
Answered by Emily J. Maths tutor

3602 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given that f(x)= (3+x^2)(x^1/2-7x). Find f'(x) (5marks)


A curve has the equation y=3x^3 - 7x^2+52. Find the area under the curve between x=2 and the y-axis.


What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?


Factorise 6x^2 + 7x - 3=0


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