MYTUTOR SUBJECT ANSWERS

1015 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...

2 years ago

Answered by Jonathan, an A Level Maths tutor with MyTutor


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

253 SUBJECT SPECIALISTS

£30 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£20 /hr

Calvin A.

Degree: Biomedical Sciences (Bachelors) - Edinburgh University

Subjects offered:Maths, Science+ 4 more

Maths
Science
Physics
Human Biology
Chemistry

“I am a friendly, passionate, enthusiastic student, studying biomedical sciences at the university of Edinburgh.”

MyTutor guarantee

£30 /hr

Alex S.

Degree: Physics (Bachelors) - Oxford, St Peter's College University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.PAT.

“Studying Physics at the University of Oxford. Looking to tutor maths and physics at all levels, be sure to send me a message if you have any questions!”

About the author

Jonathan D.

Currently unavailable: for new 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

Simplify: (3x+8)/5 > 2x + 1

Explain the Principle of Moments.

A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.

Find the integral of ln(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

mtw:mercury1:status:ok