Find the turning points and their nature of the graph y = x^3/3 - 7x^2/2 + 12x + 4

Answer = (3,17.5) maximum (4,17.33) minimum

First differentiate y = x^3/3 - 7x^2/2 + 12x + 4 to find dy/dx. Now, at turning points dy/dx = 0 and factorise to find x when dy/dx = 0. Put x back into orginal equation to find y at turning point. 

Now to find the nature of the turning point take your equation for dy/dx and differentiate again to find d^2y/dx^2. Put x of both points into this equation. If equation comes out positive the turning point is a minimum. If it comes out negative turning point is maximum. Now plot these points on a graph and see how they add up

JS
Answered by John S. Maths tutor

8429 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is calculus?


Differentiate x^3 + 6x + 1


Simplify (3 √(5))^2


A tunnel has height, h, (in metres) given by h=14-x^2 where x is the horizontal distance from the centre of the tunnel. Find the cross sectional area of the tunnel. Also find the maximum height of a truck passing through the tunnel that is 4m wide.


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