MYTUTOR SUBJECT ANSWERS

452 views

How to find the equation of a tangent to a curve at a specific point.

The first thing to remember is that the tangent to the curve at a given point has the same gradient as the curve at that point.

Let's consider the general case y=f(x) at a point c=(x1,y1).

Step 1:We have to differentiate to find dy/dx.

Step 2: Calculate dy/dx when x=x1. This is the gradient at the point c.

Step 3: Use the equation of a general straight line with gradient m at a point c 'y-y1=m(x-x1)', where m is the value of the gradient calculated in Step 2.

Here is an example. Find the equation of the tangent to the curve y=x^3-4x at the point (1,-3). 

In this example x1=1 and y1=-3

Step 1: dy/dx=3x^2-4

Step 2: When x=1, dy/dx =-1, so m=-1

Step 3: Use the equation y-y1=m(x-x1) to obtain y--3=-1(x-1)

We can then rearrange this to the nicer form of y=-x-2.

Rafe L. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

2 years ago

Answered by Rafe, an A Level Maths tutor with MyTutor


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

295 SUBJECT SPECIALISTS

£20 /hr

Matthew H.

Degree: Physics (Masters) - Liverpool University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
History
Chemistry
-Personal Statements-

“About Me  I am studying physics at the University of Liverpool and am now in my second year having passed with a first in all my modules last year. I really love all things science and have a real drive to pass on what I know to other...”

£30 /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!”

£26 /hr

Joe C.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I'm a third year student at Bristol University studying a Masters Degree in Mathematics. I try to make my tutorials engaging, and tailor them to your individual needs so that we are working towards the grade you aspire to achieve! I'v...”

About the author

Rafe L.

Currently unavailable: no new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“About Me: I am a maths student at the University of Warwick. From a young age I have always l been passionate about maths and I thoroughly enjoy teaching and helping others. I have volunteered as a football coach and as a maths tutor...”

MyTutor guarantee

You may also like...

Posts by Rafe

How to find the equation of a tangent to a curve at a specific point.

Integrating cos^2(x)+5sin^2(x)

Other A Level Maths questions

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

How to sum an arithmetic progression?

Differentiate y=x(e^x)

What is the equation of the curve that has gradient dy/dx=(4x-5) and passes through the point (3,7)?

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