What is the second derivative used for?

First of all, "second derivative", d2y/dx2, is what you get when you differentiate the first derivative (dy/dx).

The second derivative can be used as an easier way of determining the stationary points of a curve.

A stationary point on a curve can be a maximum point, a minimum point or a point of inflection. Those occur when dy/dx = 0. Once you have established where there is a stationary point, the type of stationary point (maximum, minimum or point of inflection) can be determined using the second derivative.


If d2y/dx2 (second derivative of y in terms of x)  is positive, then it is a minimum point

If d2y/dxis negative, then it is a maximum point

If d2y/dx2 is zero, then it could be a maximum, minimum or point of inflection.

If d2y/dxis 0, you must test the values of dy/dx (first derivative) either side of the stationary point, as before in the stationary points section.

If dy/dx is possitive before and negative after the stationary point then the last is a maximum. 

If dy/dx is negative before and possitive after the stationary point then the last is a minimum. 

KONSTANTINOS T. A Level Maths tutor, A Level Physics tutor, A Level G...

1 year ago

Answered by KONSTANTINOS, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£22 /hr

Bea A.

Degree: MMath Pure Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, English Literature

English Literature

“I am an experienced mathematician with a personal approach to tutoring. I'm here to help you further your mathematical potential.”

£26 /hr

Dylan P.

Degree: Chemical Engineering (Masters) - Birmingham University

Subjects offered:Maths, Science+ 3 more

-Personal Statements-

“I am a third-year student at the University of Birmingham studying my passion, Chemical Engineering. I hope to be able to inspire a similar passion in the sciences and mathematics to help you master the concepts. I am friendly and pat...”

£26 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:Maths, Further Mathematics + 3 more

Further Mathematics
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

About the author


Currently unavailable: for regular students

Degree: Civil, Environmental and Geomatic Engineering (Masters) - University College London University

Subjects offered:Maths, Physics


“I am a Master Civil Engineering Student at UCL with a first class (honours) degree. I have achived to get A* at my Maths and Physics Exams.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Differentiate y = √(1 + 3x²) with respect to x

If n is an integer prove (n+3)^(2)-n^(2) is never even.

(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

How to find y-intercept on a graphical calculator

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss