Let f(x)=2−x/1+x. Determine the y-intercept of the tangent line to the graph of f at the point (1, f (1)).

Question

Let f(x)=2−x/1+x

Determine the y-intercept of the tangent line to the graph of f at the point (1, f (1))

Answer 1

f(1) = 1/2

f^'(x) =[ -(1+x) - (2-x) ]/ (1 + x)² by quotient rule

f^'(x) = -3 / (1 + x)² ; f^'(1) = -3/4

Eqn of tangent: y - 1/2 = -3/4(x - 1). y-int: (0 , 5/4)