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...

1 year 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

Laura P.

Degree: Natural Sciences (Masters) - Lancaster University

Subjects offered: Maths


“Hi! I'm Laura, a Natural Scientist at Lancadter University, where I study Maths and Phyiscs. I have such a passion for these subjects that I hope my tutorials will be both engaging and interactive, because the best way of learning is ...”

£20 /hr

Sajidah H.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered: Maths, Further Mathematics + 2 more

Further Mathematics
-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

£22 /hr

Chris S.

Degree: Psychology (Bachelors) - Nottingham University

Subjects offered: Maths, Psychology+ 1 more

-Personal Statements-

“*Over 25 completed MyTutor school tutorials* I am a reliable and enthusiastic maths and psychology tutor.”

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

What is an Inverse function?

A circle C with centre at the point (2, –1) passes through the point A at (4, –5).....

Find the area under the curve y = (4x^3) + (9x^2) - 2x + 7 between x=0 and x=2

The Chain Rule: Differentiate (x^2 + 1)^5/2 with respect to x

View A Level Maths tutors


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