MYTUTOR SUBJECT ANSWERS

873 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

434 SUBJECT SPECIALISTS

£22 /hr

Ruth N.

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

Maths
Economics
-Personal Statements-
-Oxbridge Preparation-

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

£20 /hr

Zach T.

Degree: Aeronautics and Astronautics (Integrated Masters) - Southampton University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Extended Project Qualification
Chemistry
-Personal Statements-

“Aero and Astro Engineering student specialising in Maths and Physics A-level and GCSE.”

MyTutor guarantee

|  1 completed tutorial

£20 /hr

Harry C.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Second year Engineering student, I'm passionate, dedicated and personable. A- Level Maths and Physics (A*AA).”

MyTutor guarantee

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

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

Find, in radians, the general solution of the equation cos(3x) = 0.5giving your answer in terms of pi

Explain briefly the Normal Distribution

If n is an integer prove (n+3)^(2)-n^(2) is never even.

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