The process of obtaining the derivative of a function is called ____. Refer to the diagram given. Gradient, m = tan α. In terms of P, Q and R, what is tan α equal to? Find the gradient of the line passing through the points (1, 2) and (4, 8).

Step 1: Answer Question 1. The process of obtaining the derivative of a function is called differentiation. Answer for 1: Differentiation Step 2: Answer Question 2 by identifying the rise and run from the diagram. From the diagram, the 'rise' corresponds to the length of the segment QR, and the 'run' corresponds to the length of the segment PR. The gradient m = = riserun. Therefore, in terms of P, Q, and R: = (QR)/(PR) Answer for 2: (QR)/(PR) Step 3: Find the gradient for Question 3. The given points are (x_1, y_1) = (1, 2) and (x_2, y_2) = (4, 8). The formula for the gradient m of a line passing through two points is: m = (y_2 - y_1)/(x_2 - x_1) Substitute the given coordinates into the formula: m = (8 - 2)/(4 - 1) m = (6)/(3) m = 2 Answer for 3: 2 Drop the next question.