y = (x^3)/3 - 4x^2 + 12x find the stationary points of the curve and determine their nature.

first we find the first derivative of the function. Here dy/dx = x^2-8x+12. We set this to zero and factorise to obtain the roots of the function. Such that dy/dx = (x-6)(x-2)= 0. This gives the stationary points as x=6 and x=2. By substituting our x values into our function we can obtain the coordinates of the points. These are (6,0) and (2,32/3) To determine the nature of these points we take the second derivative of the function. d^2y/dx^2= 2x-8. By substituting our values of x into the second derivative we obtain d^2y/dx^2= 4 for x=6 and d^2y/dx^2= -4 for x=2. If the second derivative is larger than zero the point is a minima, if smaller than zero the point is a maxima. Thus (6,0) is a mimima and (2,32/3) is a maxima.

Answered by Jordan M. Maths tutor

4018 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

find f'(x) of (x^2) + 3x + 2.


What is implicit differentiation and how do I do it?


Differentiate 2x^3 - xy^2 - 4


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.


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