Consider the function (x) = (x 1) 1/3 . (a) Compute the slope of the secant

Consider the function ƒ(x) = (x − 1)^1/3.
(a) Compute the slope of the secant lines between 1 and x for x = 0.9, 0.99, 0.9999 and for x = 1.1, 1.01, 1.0001.
(b) Discuss what the secant-line slopes in (a) suggest happens to the tangent line at 1.
(c) Plot the graph of ƒ near x = 1 and verify your observation from (b).