Curve Sketching and The Extreme Value Theorem This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables. section 3-A

Critical Values Where the derivative is zero or the function does not exist.

Extreme Value Theorem The extreme value theorem states that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain both a maximum and a minimum on that interval.

1) find all extrema on the interval [0,4] a) graphically

1) cont find all extrema on the interval [0,4] b) algebraically

Find the absolute extrema and the critical values for on [-1,2] a) graphically

Cont. Find the absolute extrema and the x-values of the critical numbers for on [-1,2] b) algebraically

Find the extrema for and determine the intervals where increasing and decreasing

Curve sketching ( non calculus) Domain and Range: All real numbers except ? Intercepts: where the graph crosses the x-axis and the y-axis Symmetry About the y-axis if even function About the origin if odd function

d) Asymptotes- rational functions Vertical: set the denominator equal to zero and verify the limit tends to infinity Horizontal: Take the limit of the function as x approaches ±∞ Slant: occur when the degree of the numerator is one higher than the degree of the denominator. Use long division or synthetic division to find the line e) end behavior g) graph

4) Graph following the non-calculus curve sketching steps Domain: V.A. X-int Y-int H. A. E.B. Graph

Home Work Assignment 3-A Use a section header for each of the topics, so there is a clear transition to the audience. Assignment 3-A