Fundamental Theorem of Calculus (FTC)Expected Educational ResultsBloom’s TaxonomyUsing FTC-IInvestigation 12HomeworkCC BY-NC-SA 4.0

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

**Section 4.9**– Antiderivatives**Section 5.3**– The Fundamental Theorem of Calculus**Section 5.4**– Indefinite Integrals and the Net Change Theorem

**Objective 01–01**: I can state the*Fundamental Theorem of Calculus*.**Objective 01–02**: I can explain the meaning of the*Fundamental Theorem of Calculus*–*Part I*.**Objective 01–03**: I can explain the meaning of the*Fundamental Theorem of Calculus*–*Part II*.**Objective 01–04**: I can determine the properties of an area function using*FTC-I*and*Calculus I*.**Objective 01–05**: I can evaluate indefinite integrals using the*Fundamental Theorem of Calculus*–*Part I*.**Objective 01–06**: I can evaluate definite integrals using the*Fundamental Theorem of Calculus*–*Part II*.**Objective 01–07**: I can use the*Net Change Theorem*to identify the meaning of .${\int}_{a}^{b}{f}^{{\textstyle \phantom{\rule{0.167em}{0ex}}}\prime}(x){\textstyle \phantom{\rule{0.167em}{0ex}}}\text{d}x$ **Objective 01–08**: Given velocity of an object in motion along a line, I can find the object’s displacement and the total distance traveled.**Objective 01–09**: Given acceleration of an object in motion along a line, I can find the object’s velocity, displacement, and the total distance traveled.

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.

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

Let

Identify the graph of

. Explain.${g}^{{\textstyle \phantom{\rule{0.167em}{0ex}}}\prime}(x)$ For what value(s) of

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

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

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

, does$x$ have absolute (global) maximum(s)? Explain.$g(x)$ On what interval(s) of

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

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

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

, is$x$ concave down? Explain.$g(x)$ For what value(s) of

, does$x$ have inflection point(s)? Explain.$g(x)$

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

**Section 5.3**: # 3.

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