MYTUTOR SUBJECT ANSWERS

643 views

Find the equation of the tangent to the curve y = 2 ln(2e - x) at the point on the curve where x = e.

The first step is to find the y coordinate at the point on the curve where x = e. To do this we subsitute x = e into the equation of the curve, so y = 2ln(2e - x) becomes y = 2ln(2e - e). Simplifying this, we get y = 2ln(e). Using our knowledge of the natural logarithm, ln(e) = 1, so therefore y = 2.

Next, we find the gradient of the curve at the point x = e. We do this by differentiating the equation, and then subsituting the value for x in. Note that we have to use the chain rule.

dy/dx =  -2/(2e - x) = -2/(2e - e) = -2/e.

Using all the information we've found, we can now produce the equation of the tangent line using the equation of a line formula, y - y= m(x - x0), where m is the gradient.

y - 2 = -2/e (x - e). Rearranging this, we get y = 4 - 2x/e as the equation of the tangent line.

Rhiannon T. GCSE Maths tutor, A Level Maths tutor

1 year ago

Answered by Rhiannon, an A Level Maths tutor with MyTutor


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

258 SUBJECT SPECIALISTS

£24 /hr

Runzhi C.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi there, I am an experienced tutor for Biology and Maths. A money-back guarantee is provided if you are not 100% happy with the session. ”

£22 /hr

Shreya G.

Degree: Biochemistry with molecular medicine (Bachelors) - Nottingham University

Subjects offered:Maths, Biology+ 1 more

Maths
Biology
-Personal Statements-

“I am a first year undergraduate student at The University Of Nottingham, currently studying Biochemistry with molecular medicine. ”

£24 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I study Maths at York University; I chose York because I loved the lecturers, they made maths fun and easy- that's what I hope to do with all my students!”

About the author

Rhiannon T.

Currently unavailable: until 02/02/2017

Degree: Mathematics (Bachelors) - Cardiff University

Subjects offered:Maths

Maths

“I am currently in my second year of studying Maths at Cardiff Universty. I love my subject and as a tutor I hope to inspire and instill that love within my students. I'm laid back, friendly, and love to teach. I have been doing Taekwo...”

You may also like...

Other A Level Maths questions

give the coordinates of the stationary points of the curve y = x^4 - 4x^3 + 27 and state with reason if they are minumum, maximum, or points of inflection.

Find minimum and maximum of x^2+1 if they exist

How do I draw and sketch an equation?

How do you solve 3sin2AtanA=2 for 0<A<180?

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