MYTUTOR SUBJECT ANSWERS

175 views

Find the equation of the tangent to the curve y=x^3-4x^2+2 at the point (3,-7)

y=x3-4x2+2

A tangent to a curve at a specific point along the line will have excatly the same gradient as the curve at that point. For example if the point was (0,0) the tangent would just be a horizontal line along the x-axis. To work out the gradient we simply differentiate the curve, set this to equal 0 and solve with the given value of x. 

Here dy/dx = 3x2-8x

Setting this to 0 and solving gives us 3(3)2-8(3)=3 and so our gradient at the point (3,-7) is 3

We are now able to use the equation y-y(1)=m(x-x(1)) where m is the gradient and x(1) & y(1) are the coordinates we've been given. 

Rearranging we get y=3(x-3)-7

y=3x-16 and this is the equation of the tangent to the curve y=x3-4x2+2 at the point (3,-7)

Daniel W. A Level Maths tutor, GCSE Maths tutor, GCSE Chemistry tutor

4 months ago

Answered by Daniel, an A Level Maths tutor with MyTutor


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

183 SUBJECT SPECIALISTS

£20 /hr

Solomon L.

Degree: Mathematics (Bachelors) - Leeds University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Currently studying at Leeds university, ready to help you improve your grades in Maths and Chemistry GCSE! ”

£20 /hr

Fraser F.

Degree: Mathematics (Masters) - Durham University

Subjects offered: Maths

Maths

“Hi, I'm Fraser! I'm a third year student at Durham University working towards a masters in mathematics. I've loved learning about maths and I hope I am able to pass that on to anyone I tutor. Sessions will be focussed around your needs...”

MyTutor guarantee

£22 /hr

Alex B.

Degree: Physics (Masters) - Durham University

Subjects offered: Maths, Physics

Maths
Physics

“About me: I’m Alex and I have just completed my first year studying physics at Durham University, with a first. I have a passion for mathematics and how it can be applied to solve problems in physics. Throughout my A levels, other stu...”

About the author

£22 /hr

Daniel W.

Degree: Chemistry and Maths (Bachelors) - Leeds University

Subjects offered: Maths, Chemistry

Maths
Chemistry

“Me, Myself & I I am studying Chemistry and Maths at the University of Leeds and I am about to go into the second year of my degree. From quite an early age I realised Maths and Science are where my interests lie.  I volunteered as a ...”

You may also like...

Other A Level Maths questions

G(x)=x^3 + 1, h(x)=3^x; solve G(h(a))=244

If y = (4x^2)ln(x) then find the second derivative of the function with respect to x when x = e^2 (taken from a C3 past paper)

Differentiate y=x(e^x)

Prove that the derivative of tan(x) is sec^2(x).

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