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


£20 /hr

Elliot D.

Degree: Mathematics (Bachelors) - St. Andrews University

Subjects offered:Maths, Physics


“Hi, I'm a 2nd year Computer Science student at St Andrews University. I mainly teach Maths at both GCSE and A-level.”

Sahil M. A Level Biology tutor, GCSE Biology tutor, A Level Chemistry...
£22 /hr

Sahil M.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered:Maths, Spanish+ 3 more

-Medical School Preparation-

“Hello! My name is Sahil and I am currently a medical student at the University of Manchester. I am really looking forward to tutoring you in Spanish, Chemistry, Biology or Maths as well as trying to help you during the difficult proce...”

£20 /hr

Kai A.

Degree: Physics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics

“Hi! My name is Kai and I study physics at Bristol. I am happy to tutor in maths, further maths, physics and the PAT.”

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

How do you find the integral of sin^2(x) dx?

Find the exact value of the gradient of the curve y = e^(2- x)ln(3x- 2). at the point on the curve where x = 2.

How can I integrate the function f(x) = x sin(x)?

What is the gradient of y = xcos(x) at x=0?

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