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


Visitation L. GCSE Biology tutor, GCSE Maths tutor, A Level Biology t...
View profile
£20 /hr

Visitation L.

Degree: Biomedical sciences (Bachelors) - Durham University

Subjects offered: Maths, Biology


“Hi, I am Visitation, a second year Biomedical scientist at Durham. Science and Maths are such fascinating subjects and I would like to share my passion and help you through my tutorials!”

Sophie K. GCSE Maths tutor, Mentoring -Personal Statements- tutor, A ...
View profile
£20 /hr

Sophie K.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered: Maths, History+ 2 more

English Literature
-Personal Statements-

“About Me Hi, I'm Sophie and I'm a Maths student at the University of Birmingham. I have always had a passion for maths due to the satisfaction you get from obtaining the one correct answer and the amount of real world applications it ...”

PremiumChristopher S. A Level Maths tutor, GCSE Maths tutor, A Level Spanish...
View profile
£26 /hr

Christopher S.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Spanish+ 1 more

Further Mathematics

“ I am extremely passionate about mathematics and I love the Spanish language! ”

About the author

James S. A Level Maths tutor, A Level Physics tutor, A Level Further ...
View profile
£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

What's the integral of x^2 +3/x, with respect to x?

How should I aproach a connected rates of change question.

Line AB has the equation 3x + 5y = 7. Find the gradient of Line AB.

How to solve a quadratic equation?

View A Level Maths tutors


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