Equation of a tangent line

Question

Answer 1

Let f(x) = 2x/(x-1)

Use quotient rule to find f'(x) = [(x-1)(2) - (2x)(1)] / (x-1)²

Plug in x=-1 to find f'(-1) = [(-1-1)(2) - (2*-1)(1)] / (-1-1)²

So f'(-1) = [-4-(-2)]/(-2)²

f'(-1) = -2/4= -1/2

We now use the point-slope form equation: y-y₁ = m(x-x₁)

So then we have y-1 = -1/2(x+1) using point slope form and m=f'(-1)