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
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.