State briefly the steps involved to find the equation of a tangent to the curve.

2 years ago


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Alysa Senger

2 Answers

Freddie Melbourne

A tangent is a straight line which has the same gradient as the curve at a given point.

In order to find the gradient:

  1. Differentiate the equation of the curve to find the general equation of the gradient.
  2. Input the x coordinate of the point given, to find the specific value of the gradient at this point- and therefore the gradient of the tangent.
  3. You have the gradient of the line (m) and a point on the line (x1, y1), so now you can use the equation: y - y1 = m(x-x1). Rearrange this to get the desired form of the equation of the tangent!
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suppose the tangent touch the curve at the point (x1,y1).

step1: differentiate the curve

step2: substitute x1 and y1 into the differential which gives you the gradient.

step 3: substitute into y-y1 = m(x-x1) where m is the gradient and rearrange to give y=.....

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