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.