Consider y = x2 + 1.
(a) Sketch its graph as carefully as you can.
(b) Draw the tangent line at (1, 2).
(c) Estimate the slope of this tangent line.
(d) Calculate the slope of the secant line through (1, 2) and (1.01, (1.01)2 + 1.0).
(e) Find by the limit process (see Example 1) the slope of the tangent line at (1, 2).