It’s also important to check the endpoints of an interval, if these make sense in the context of the problem, since these points could also be the minimum or maximum to get the absolute extrema. Typically, to get the domain of a problem, we find the $ x$-values that would “make sense” for example, we can’t have a dimension of 0 or less. With optimization, if we have more than one critical point, we need to check the candidates to see which one is the absolute extrema in the possible domain (values that the “$ x$” can be). In the Curve Sketching section here, we learned that a critical number is where the function’s derivative is 0, or not defined and from the First Derivative Test, critical numbers exist at relative minimums or maximums (also called local minimums or maximums). We can also take the second derivative of the function to verify that the function is a minimum (“cup up”, or positive 2 nd derivative) or maximum (“cup down” or negative 2 nd derivative). We first learned about Relative and Absolute Minimums and Maximums here in the Advanced Functions section. Let’s first revisit absolute extrema, which are the absolute minimum and maximum of a function on an interval. Some examples of optimization include finding the greatest profit, least cost, greatest volume, optimum size, greatest strength, and so on. We call this optimization, since we are typically finding the optimal or “best value” for something. One that is very useful is to use the derivative of a function (and set it to 0) to find a minimum or maximum to find either the smallest something can be, or the largest it can be. Applications of Integration: Area and VolumeĪs we’ve seen before, there are many useful applications of differential calculus.Exponential and Logarithmic Integration.Riemann Sums and Area by Limit Definition.Differential Equations and Slope Fields.Antiderivatives and Indefinite Integration, including Trig.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, Error Propagation.Curve Sketching, Rolle’s Theorem, Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Rates of Change.Differential Calculus Quick Study Guide.Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear, Angular Speeds, Area of Sectors, Length of Arcs.Conics: Part 2: Ellipses and Hyperbolas. Graphing and Finding Roots of Polynomial Functions.Graphing Rational Functions, including Asymptotes.Rational Functions, Equations, and Inequalities.Solving Systems using Reduced Row Echelon Form.The Matrix and Solving Systems with Matrices.Advanced Functions: Compositions, Even/Odd, Extrema.Solving Radical Equations and Inequalities.Solving Absolute Value Equations and Inequalities.Imaginary (Non-Real) and Complex Numbers.Solving Quadratics, Factoring, Completing Square.Introduction to Multiplying Polynomials.Scatter Plots, Correlation, and Regression.Algebraic Functions, including Domain and Range.Systems of Linear Equations and Word Problems.Introduction to the Graphing Display Calculator (GDC).Direct, Inverse, Joint and Combined Variation.Coordinate System, Graphing Lines, Inequalities.Types of Numbers and Algebraic Properties.Introduction to Statistics and Probability.Powers, Exponents, Radicals, Scientific Notation.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |