18.01, Calculus, Problem Set 1

Problems to be collected, February 11. • §2.2: 5, 8

• Use the geometric interpretation of the derivative to explain why the derivative of a linear function is a constant function. (Use words and possibly pictures, but no formulas. Do not use pronouns.)

• §2.3: 1, 6, 18, 26

• Sketch the graph of f(x) = x|x|. From the graph, predict the value of f′(0). Verify this prediction using the definition of the derivative.

• §2.4: 2, 8

• p.81: 14

• §2.5: 2, 4, 9, 10, 14, 25

• Give an example of a function which is continuous at every point, and is differentiable at every point except x = 1 and x = −1.