Fundamental Theorem of Calculus (FTC)

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Bloom’s Taxonomy

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Bloom’s Taxonomy for different levels of understanding
Figure 1.1: Bloom's Taxonomy

Using FTC-I

Investigation 12

Use what you learned from Activity 11 to answer the following:

Let g(x)=axf(t)dt, where the graph of f(t) is shown below:

  1. Identify the graph of g(x). Explain.

  2. For what value(s) of x, does g(x) have relative (local) minimum(s)? Explain.

  3. For what value(s) of x, does g(x) have relative (local) maximum(s)? Explain.

  4. For what value(s) of x, does g(x) have absolute (global) minimum(s)? Explain.

  5. For what value(s) of x, does g(x) have absolute (global) maximum(s)? Explain.

  6. On what interval(s) of x, is g(x) increasing? Explain.

  7. On what interval(s) of x, is g(x) decreasing? Explain.

  8. On what interval(s) of x, is g(x) concave up? Explain.

  9. On what interval(s) of x, is g(x) concave down? Explain.

  10. For what value(s) of x, does g(x) have inflection point(s)? Explain.

Homework

At this time, you should be able to complete the following assignments:

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Created: Tuesday, 25 August 2020 03:31 EDT Last Modified: Monday, 10 January 2022 - 06:37 (EST)