advertisement

MATH1210: Midterm 2 Study Guide The following is an overview of the material that will be covered on the first exam. §2.9 Differentials and Approximations • The definition of differentials. • Approximating increments by differentials. f (x + ∆x) ≈ f (x) + dy = f (x) = f 0 (x)∆x §3.1 Maxima and Minima • The definition of a global maximum or minimum and an extreme value. • The Max-Min Existence Theorem. This is the one that says a continuous function on a closed interval always has a max and a min. • The Critical Point Theorem. This says that maxima and minima always happen at critical points. §2.2 Monotonicity and Concavity • The (intuitive) definition of an increasing or decreasing function. • The Monotonicity Theorem. • The definition of concavity. • The Concavity Theorem. • The definition of an inflection point. Know how to identify inflection points from the graph of a function (See pg1̇59 in textbook). §3.3 Local Extrema and Extrema on Open Intervals • The definition of a local maximum or minimim as well as the definition of a local extreme value. • The First Derivative Test. • The Second Derivative Test. §3.4 Practical Problems • You should be able to apply the theorems of the previous 3 sections to “real world” problems. §3.5 Graphing Functions Using Calculus • I guarantee that there will be a graphing problem on the exam. It will be worth 2030 points. Know how to apply the methods of calculus to draw a detailed graph of a function. See example 1 in §3.5. §3.6 The Mean Value Theorem for Derivatives • The Mean Value Theorem for Derivatives. 1 • Using the Mean Value Theorem for Derivatives. §3.7 Solving Equations Numerically • The Bisection Method for finding solutions to f (x) = 0. • Newton’s Method for finding solutions to f (x) = 0. • The Fixed Point Method for solving g(x) = x. §3.8 Antiderivatives • Know how to compute indefinite integrals, including using the power rule and the “Generalized Power Rule” (in class I called this “the chain rule backwards”). • Don’t forget the integration constant, C. 2