Find the stationary point of y=3x^2-12x+29 and classify it as a maximum/minimum

The stationary point of a curve is where it changes direction, that is the gradient goes from positive to negative or vice versa. At the exact point of the change, the gradient of the curve will be exactly 0.

This means we need to differentiate the equation of the curve and find the point at which the derivative is equal to 0. Using the rule that a*x^b differentiates to ab*x^(b-1) we get:


Setting this equal to 0 we get:




Subbing this value of x into the original equation we find the y-value to be 17

This means the stationary point is the point (2,17)

To classify this point as a maximum/minimum we must examine the second derivative. We know that if the second derivative is positive the point is a minimum and if it is negative the point is a maximum. 

Differentiating (dy/dx)=6x-12 we get:


As this is always positive, we can classify the stationary point (2,17) as a minimum.

- See more at:

James S. A Level Maths tutor, A Level Physics tutor, A Level Further ...

2 years ago

Answered by James, an A Level Maths tutor with MyTutor

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


Roma V. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, ...
£26 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£22 /hr

Chris S.

Degree: Psychology (Bachelors) - Nottingham University

Subjects offered:Maths, Psychology+ 1 more

-Personal Statements-

“*Over 25 completed MyTutor school tutorials* I am a reliable and enthusiastic maths and psychology tutor.”

£22 /hr

Ellen H.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, English Literature+ 2 more

English Literature

“Hello! My name is Ellen, and I'm a Maths student at the University of Bristol. I'm here to help, so just send me a message!”

About the author

£20 /hr

James S.

Degree: Mathematics and Physics (MSci) (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“First year Maths and Physics undergraduate at Durham University. Previous tutoring experience with A-level students”

MyTutor guarantee

You may also like...

Posts by James

A given star has a peak emission wavelength of 60nm, lies 7.10*10^19m away and the intensity of its electromagnetic radiation reaching the Earth is 3.33*10^-8Wm^-2. Calculate the star's diameter

Find the stationary point of y=3x^2-12x+29 and classify it as a maximum/minimum

Using mathematical induction, prove that n^3+2n is divisible by 3 for all integers n

Other A Level Maths questions

How would you differentiate ln(sin(3x))?

Differentiate x^2 + y^2 with respect to x

Differentiate y = (3x − 2)^4

How do I multiply complex numbers?

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