MYTUTOR SUBJECT ANSWERS

480 views

What is a stationary point and how do I find where they occur and distinguish between them?

A stationary point is simply a point on a graph where the derivative=0. Ie, the rate of change of the curve at this point is 0 and therefore it is neither increasing or decreasing at this point

There are three types you need to know about:

1) A maximum: Here the derivative =0 and the second derivative <0.

2) A minimum: Here the derivative =0 and the second derivative >0

3) A point of inflection: Here the derivative and the second derivative =0

Note, the second derivative means the derivative of the first derivative!

General solution:

Suppose y=f(x)

and dy/dx=f'(x)

If at a point, say c, f'(c)=0 then there is a stationary point at this value of x.

Differentiate f'(x) to get the second derivative.

Plug in the value of c again and if the solution is..

0 - Point of inflection

Positive - Minimum turning point

Negative - Maximum turning point

Example

y = x3 - 6x2 + 9x - 4

Find any stationary points and determine their nature.

Solution 

dy/dx = 3x2- 12x + 9

At a stationary point, dy/dx=0

So 3x2- 12x + 9 = 0

3(x2- 4x + 3) = 0  

(x - 3)(x - 1) = 0

So stationary point at x = 3 and x = 1.

Now, to determine the nature of these..

f''(x) = 6x - 12

f''(3) = 18 - 12 = 6 therefore minimum turning point at x = 3

f''(1) = 6 - 12 = -6 therefore maximum turning point at x = 1

Anna H. GCSE Biology tutor, A Level Biology tutor, GCSE Maths tutor, ...

2 years ago

Answered by Anna, an A Level Maths tutor with MyTutor


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

260 SUBJECT SPECIALISTS

£26 /hr

Jonathan A.

Degree: Economics (Masters) - University College London University

Subjects offered: Maths, Philosophy+ 4 more

Maths
Philosophy
Government and Politics
Economics
.TSA. Oxford.
-Oxbridge Preparation-

“About Me: I am studying for an MSc in Economics at University College London.  I did my undergraduate degree in Oxford studying Philosophy, Politics and Economics, and as a result amfamiliar with the tutorial system from the student's...”

£22 /hr

Daniel W.

Degree: Chemistry and Maths (Bachelors) - Leeds University

Subjects offered: Maths, Chemistry

Maths
Chemistry

“Me, Myself & I I am studying Chemistry and Maths at the University of Leeds and I am about to go into the second year of my degree. From quite an early age I realised Maths and Science are where my interests lie.  I volunteered as a ...”

£20 /hr

Sajidah H.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered: Maths, Further Mathematics + 2 more

Maths
Further Mathematics
Biology
-Personal Statements-

“I am a Mathematics student at the University of Birmingham. I have a genuine love for Maths and eventually want to go on to teach it to young people. I am friendly and very patient, and if you’re struggling, we’ll work together to fin...”

MyTutor guarantee

About the author

£22 /hr

Anna H.

Degree: Natural Sciences with Year Abroad (Bachelors) - Durham University

Subjects offered: Maths, Biology

Maths
Biology

“Experienced tutor from Durham University, ready to help you improve your grades.”

You may also like...

Other A Level Maths questions

How do I solve equations like 3sin^2(x) - 2cos(x) = 2

A curve C has equation y=(2x-3)^5. Find the equation of the normal of this curve at point P with y coordinate -32.

For rectangles of area 100 m^2 what is the perimeter of the rectangle with the smallest perimeter?

What is a parametric equation?

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