MYTUTOR SUBJECT ANSWERS

570 views

How do you find the equation of a tangent to a curve at a particular point?

Imagine being given the equation y=x3-2x+3, and being asked to find the tangent to the curve at the point where x=1.

The tangent to the curve will be a straight line, and therefore will take the form y=mx+c.

To find m (the gradient of the tangent), it is necessary first of all to differentiate the equation of the original curve. Doing this gives y’=3x2-2, where y’ is the gradient of the curve at a particular point. We are looking for the gradient at the point where x=1. Therefore, to find m, we must substitute x=1 into our expression. Doing so, we find that m=1.

We now know the equation of the tangent is y=x+c. To find c (the y-intercept), we must first of all know the coordinates of a point that the tangent is going to pass through. In our case, we know that the tangent must pass through the point on the line where x=1. To find the y-coordinate of this point, we can sub x=1 into our original equation of the curve. Doing so, we find that the point we must use is (1,2).

Now that we know a point on the line, we can sub those x and y values into the expression y=x+c. This gives us the equation 2=1+c, and some quick rearrangement shows us that c=1.

Therefore the equation of the tangent is y=x+1.

In summary:

-Equation of tangent is of the form y=mx+c

-To find m, differentiate the equation of the curve to find its gradient at the required point

-Find the coordinates of a point the tangent is going to pass through, and sub into the equation of the tangent to find c.

Jonathan D. A Level Maths tutor, GCSE Physics tutor, GCSE Chemistry t...

1 year ago

Answered by Jonathan, an A Level Maths tutor with MyTutor


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

176 SUBJECT SPECIALISTS

£22 /hr

Julia L.

Degree: Economics L100 (Bachelors) - Durham University

Subjects offered: Maths, Sociology+ 2 more

Maths
Sociology
Russian
Economics

“Hi! My name is Julia, and I am Durham University student. I have just been through the stress of A level exams - I've been in your shoes, so now, my goal is to make your exam time as smooth and painless as it can be. I can help you wi...”

£20 /hr

Oliver T.

Degree: Mathematics (Masters) - Edinburgh University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hello! I'm currently a 2nd year Mathematics student at the University of Edinburgh with a sturdy passion for all things Mathematics. Not only do I love Maths, I love teaching Maths and helping people with problems. In particular, I en...”

£20 /hr

Daniel S.

Degree: MEng Mechanical Engineering (Masters) - Exeter University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Dan and I am currently on the Masters Mechanical Engineering course at Exeter University. I studied Maths, Further Maths and Physics at A-level and recieved A*AA grades for them. I love helping people understand maths and I fi...”

MyTutor guarantee

About the author

Jonathan D.

Currently unavailable: for regular students

Degree: Natural Sciences (Physical) (Bachelors) - Cambridge University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“2nd year Natural Sciences student at Cambridge - massively passionate about all things Maths and Science, and I would love to be able to help!”

You may also like...

Other A Level Maths questions

How to find out where 2 lines cross/simultaneous equations

M1: A stationary rock is dropped from a height of 30m above the ground. Calculate the time taken to reach the ground and its velocity as it hits the floor.

What is a stationary point on a curve? How do I calculate the co-ordinates of a stationary point?

How do I use the chain rule to differentiate polynomial powers of e?

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