Question 6.1.1: Find f '(1), f '(4), and f '(7) for the function whose graph......

At the point P = (1, 2), the tangent goes through the point (0, 1), and so has slope 1. At the point Q = (4, 3) the tangent is horizontal, and so has slope 0. At the point R = (7, 2\frac{1}{2}), the tangent goes through (8, 2), and so has slope −1/2. Hence, f ^{\prime}(1) = 1, f^{\prime}(4) = 0, and f^{\prime}(7) = −1/2.