We know that the slope of the line is 2. So therefore, all we have to do is find the point at which a line tangent to the curve , and then determine the equation of this line, knowing that it's slope is 2.

So, how do we do this? we know that the slope of a line that goes throgh any 2 points on the curve is given by , or in functional notation . But this is only 2 points that goes through the curve, it is not the tangent line. To find the tangent line to a curve at any point on the curve, we'd have to take the limit as tends to 0. Or

.

So, Let's do it.

=

after multiplying and adding we have

Factoring out

Taking the limit by substituting for we get

and we have a formula for finding the slope at any point on the curve of .

setting our formula equal to 2 allows us to solve for x

Now all you have to do is sub

into to obtain the corresponding values of , and knowing that the slope of the line tangent to the curve at that point is 2, you can write an equation to that line.