MYTUTOR SUBJECT ANSWERS

1037 views

How do I find where the stationary points of a function are?

If you were to draw a graph of the function, a stationary point would be a point on the graph where the gradient is zero, i.e the graph has no vertical slope. For example consider the function f(x) = 2. This is a graph where every  value of x simply takes the y value of 2, and thus is just the horizontal line y=2. This graph has zero gradient everywhere, and hence every point on the graph is a stationary point. 

In general, if we have a function y=f(x), we must differentiate it first in order to find the stationary points. Once we have differentiated, we have an expression of the form dy/dx=f'(x). The solutions to the equation dy/dx=0 are the x values of where the stationary points occur. We then subsitute these x values into the expression y=f(x) to find the corrresponding y values to each x value. This will give us the coordinates for each stationary point.

Example

Consider the function f(x)=x^3 -12x. We let y=f(x). We must now differentiate to get an expression of the form dy/dx = f'(x). Differentiating our function with respect to x we have that f'(x)= 3x^2 - 12. Hence our expression for dy/dx is dy/dx=3x^2 - 12. We must now solve the equation dy/dx=0 in order to find the x values of the stationary points. We have 3x^2 - 12 =0 as our equations. Dividing both sides by 3, we now have x^2 - 4=0, and factorising this expression using the 'Difference of Two Squares' method, we have that (x-2)(x+2)=0. Hence our two x value are 2 and -2. When x=2, f(x)= 3(2^2)-12(2)=-12. So one coordinate is (2,-12). When x=-2, f(x)=3((-2)^2) - 12(-2) = 36. So the other coordinate is (-2,36).

Hence by differentiating y=f(x), solving the equation dy/dx=0 and then substituting in the solutions of this equation into our expression f(x), we have found that the coordinates of the stationary points are (2,-12) and (-2,36)

Laasya S. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...

2 years ago

Answered by Laasya, who has applied to tutor A Level Maths with MyTutor


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

307 SUBJECT SPECIALISTS

£22 /hr

Lucy S.

Degree: Chemistry (Masters) - Durham University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Reading Chemistry at Durham University with expertise in Chemistry and Mathematics (A*A*) at GCSE/A-level”

£36 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I study General Engineering at the University of Durham. I have always enjoyed maths and sciences, so hope to help students who share my love for them too!”

£20 /hr

Adamos S.

Degree: Electrical and Electronic Engineering (Masters) - Imperial College London University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Electronics

“Degree: Electrical and Electronic Engineering (Masters) University: Imperial College London ”

About the author

£20 /hr

Laasya S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

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

MyTutor guarantee

You may also like...

Posts by Laasya

How do I differentiate sin^2(x)?

How do I find where the stationary points of a function are?

Other A Level Maths questions

How do I find the coordinates of maximum and minimum turning points of a cubic equation?

A Definitive Guide to Differentiation

integrate [xe^(-x)] with respect to x.

A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.

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

mtw:mercury1:status:ok