1. Differentiability Versus Continuity 2 2. Differentiation Rules 3 3. Optimization 7 3.1. Intervals and interior points 7 3.2. Functions increasing or decreasing at a point 7 3.3. Extreme Values 8 3.4. Local Extrema and a Procedure for Optimization 10 3.5. Remarks on finding roots of f ′ 12 4. The Mean Value Theorem 12 4.1. Statement of the Mean Value Theorem 12 4.2. Proof of the Mean Value Th...