The curve y = x/(1 + x2) is called a serpentine. find an equation of the tangent line to this curve at the point (2, 0.40). (round the slope and y-intercept to two decimal places.) y =

One way of solving this is using calculus: derivatives.

We have . Let's take this as a function of x.

So, 

.

Now, we find it's derivative: f'(x). To do this, we use the quotient rule. The derivative [ f'(x) ] basically gives us the slope of the tangent line at a point x.



Now, we evaluate the derivative at the point x = 2 to find the slope of the tangent line at that point.


Now, we have the slope and the x and y co-ordinates; thus, we can use the point slope form to find the equation of the tangent line at the point (2,0.40).







That's the equation.