A) if f(x) = 6x/(2 + x2), find f '(2) and use it to find an equation of the tangent line to the curve y = 6x/(2 + x2) at the point (2, 2). f '(2) = incorrect: your answer is incorrect. y(x) =

So we're trying to construct a line,
a tangent line to be more precise.
y = mx + b

The derivative evaluated at 2 gives us the SLOPE of that line.
f'(2) = m

Apply your quotient rule to get the derivative of f,





Don't bother simplifying.
Plug your location in at this point, it will be easier to simplify once everything is numbers:



which simplifies to something like 1/3.
This is the slope of our tangent line, m = 1/3.

y = (1/3)x + b

Since they gave you a point, and we just found our slope,
it might make more sense to put your line in Point-Slope form.

y - y0 = m(x - x0)

y - 2 = (1/3)(x - 2)

If you need your final answer in Slope-Intercept form,
then simply solve for y from this point.