MA.912.C.1.11

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Apply the Intermediate Value Theorem and the Extreme Value Theorem.

Examples

Example: Use the Intermediate Value Theorem to show that begin mathsize 12px style g left parenthesis x right parenthesis space equals space x cubed plus 3 x squared minus 9 x minus 2 end style has a zero between x=0 and x=3. 

Example: Use the Extreme Value Theorem to decide whether f(x)=tan(x) has a minimum and maximum on the interval begin mathsize 12px style open square brackets table row cell negative straight pi over 4 comma end cell cell straight pi over 4 end cell end table close square brackets end style. What about on the interval begin mathsize 12px style open square brackets table row cell negative straight pi comma end cell straight pi end table close square brackets end style?

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Calculus
Standard: Develop an understanding for limits and continuity. Determine limits and continuity.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))

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