`f(x) = 6/(x + 2), (0, 3)` Find an equation of the tangent line to the graph of f at the given point.

Expert Answers
hkj1385 eNotes educator| Certified Educator

The given function is:-

f(x) = 6/(x+2)

differentiating both sides w.r.t 'x' we get

f'(x) = -6/{(x+2)^2} 

Now, slope of the tangent at the point (0,3) = f'(0) = -6/4 = -3/2

Thus, equation of the tangent at the point (0,3) and having slope = -3/2 is :-

y - 3 = (-3/2)*(x-0)

or, 2y - 6 = -3x

or, 2y + 3x = 6 is the equation of the tangent to the  given curve at (0,3)