Find the equation of the tangent to the curve (y = frac{x – 1}{2x + 1}, x neq -frac{1}{2}) at the point (1, 0).
Explanation
(y = frac{x – 1}{2x + 1}, x neq -frac{1}{2})
Using the quotient rule, we have
(frac{mathrm d y}{mathrm d x} = frac{(2x + 1). 1 – (x – 1). 2}{(2x – 1)^{2}})
= (frac{2x + 1 – 2x + 2}{(2x + 1)^{2}})
(frac{mathrm d y}{mathrm d x} = frac{3}{(2x + 1)^{2}})
At (1, 0), (frac{mathrm d y}{mathrm d x} = frac{3}{(2(1) + 1)^{2}} = frac{3}{9} = frac{1}{3})
Equation : (frac{y – 0}{x – 1} = frac{1}{3})
(y = frac{1}{3}(x – 1))