The curve C has the equation y = 2x^2 -11x + 13. Find the equation of the tangent to C at the point P (2, -1).

  • Google+ icon
  • LinkedIn icon
  • 752 views

The first step is to differentiate the equation of the curve in order to find the gradient of the tangent at the curve. Remember that when differentiating polynomials, we multiply the index of the variable x, by its coefficient, then subtract 1 from the index. In addition, remember that x0 = 1.

In this case, dy/dx = 4x - 11.

Now if we plug in the x-coordinate of P (2) into dy/dx, we will get the gradient of the tangent to the curve at P.

dy/dx = 4(2) - 11

dy/dx = 8 - 11

dy/dx = -3.

Now we find the equation of the tangent using the formula for the equation of a straight line, and plugging in the coordinates of P:

y - y= m(x - x1)

y - (-1) = -3(x - 2)

y + 1 = -3x +6

3x + y - 5 = 0.

This is the equation of the tangent to the curve C at P.

James Y. A Level Maths tutor, GCSE Maths tutor, A Level Further Mathe...

About the author

is an online A Level Maths tutor with MyTutor studying at Exeter University

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

95% of our customers rate us

Browse 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