Verify that P = (1, 1/2) lies on the graphs of both (x) = 1/(1 + x

Verify that P = (1, 1/2) lies on the graphs of both ƒ(x) = 1/(1 + x²) and L(x) = 1/2 + m(x − 1) for every slope m. Plot y = ƒ(x) and y = L(x) on the same axes for several values of m until you find a value of m for which y = L(x) appears tangent to the graph of ƒ. What is your estimate for ƒ'(1)?