Question

derivative Question

Answer 1

A curve like
y=(x/(1+3x^2)
is a called serpentine.
Find an equation of the tangent line to this curve at the point
(3,3/28)

Answer 2

Just differentiate...then plug in x = 3. This gives you the slope of the tangent line at that point. Then use that:
\[y-y_0 = m(x-x_0)\]
Where:
\[(x_0,y_0) = \left(3,\frac{3}{28}\right)\]