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


£20 /hr

Liam R.

Degree: Economics (Bachelors) - Durham University

Subjects offered:Maths


“I study Economics at Durham. I have a passion for maths and hope to share this with you! To find out more, click on my profile & book a free 15-minute meeting!”

£22 /hr

Laura L.

Degree: Chemistry (MCHEM) (Masters) - Warwick University

Subjects offered:Maths, Chemistry+ 1 more


“Hi there! I'm a third-year Chemistry student, I tutor maths from 11+ to A level as well as GCSE Science, A level Biology, and Chemistry”

£20 /hr

Juris B.

Degree: Computer Science (Bachelors) - St. Andrews University

Subjects offered:Maths, Computing


“I am a Computer Science at the University of St. Andrews. Before that however, I was a pupil in a school in the North-East of Scotland. With the combined passion and availability of superb teachers - I was given an opportunity to exce...”

About the author

Rafe L.

Currently unavailable: no new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

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

How do I find the distance between two point in the plane?

Integrate (x)(e^x) with respect to x and then integrate (x)(e^x) with respect to y.

How do you differentiate y=sin(cos(x))?

Differentiate x^5 + 3x^2 - 17 with respect to x

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