In this, the third section of the course, the topics include:
Applications of derivatives
• Analysis of curves, including the notions of monotonicity and concavity.
• Optimization, both absolute (global) and relative (local) extrema.
• Modeling rates of change, including related rates problems.
• Use of implicit differentiation to find the derivative of an inverse function.
• Interpretation of the derivative as a rate of change in varied applied contexts,
including velocity, speed, and acceleration.
• Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations.
Computation of derivatives
• Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
• Derivative rules for sums, products, and quotients of functions.
• Chain rule and implicit differentiation.