MYTUTOR SUBJECT ANSWERS

587 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...

1 year 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

254 SUBJECT SPECIALISTS

£20 /hr

Marcus J.

Degree: Mathematics (Masters) - Exeter University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Little bit about me:I'm a first year maths student at Exeter. With a excitement for all things mathematics I have helped teach at many different levels in the past! I hope my patience, friendlieness and entusiasm comes across in the ...”

MyTutor guarantee

£20 /hr

Steven K.

Degree: Material Science (Masters) - Oxford, The Queen's College University

Subjects offered: Maths, -Personal Statements-

Maths
-Personal Statements-

“I started tutoring through my father who is a maths teacher, as he would pass on requests for lessons to me. Through my A levels I tutored GCSE maths, and began to also teach physics, chemistry and biology, the other subjects i was st...”

£20 /hr

Amelia F.

Degree: Social Anthropology MA (Bachelors) - Edinburgh University

Subjects offered: Maths, Extended Project Qualification+ 1 more

Maths
Extended Project Qualification
English Literature

“I am a Social Anthropology student at the University of Edinburgh. I have always had a passion for learning and for helping others and I am hoping that I will be able to give my love of education back to my students. I am very patient...”

MyTutor guarantee

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

A curve is defined by the parametric equations x=t^2/2 +1, y=4/t -1. Find the gradient of the curve when t =2.

What is an easy way to remember how sin(x) and cos(x) are differentiated and integrated?

Given that dy/dx=6-8x+x^4 and that x=1 when y=4. Find an expression for y in terms of x.

Solve the equation 3^(5x-2)=4^(6-x), and show that the solution can be written in the form log10(a)/log10(b).

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok