Intermediate Value Theorem

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# Intermediate Value Theorem - PowerPoint PPT Presentation

Intermediate Value Theorem. Objective : Be able to find complex zeros using the complex zero theorem &amp; be able to locate values using the IVT TS : Explicitly assess information and draw conclusions.

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### Intermediate Value Theorem

Objective: Be able to find complex zeros using the complex zero theorem & be able to locate values using the IVT

TS: Explicitly assess information and draw conclusions

Warm Up: Refresh your memory on what the complex zero theorem says then use it to answer the example question.

Complex Root Theorem: Given a polynomial function, f, if a + bi is a root of the polynomial then a – bi must also be a root.
Intermediate Value Theorem (IVT): Given real numbers a & b where a < b. If a polynomial function, f, is such that f(a) ≠ f(b) then in the interval [a, b] f takes on every value between f(a) to f(b).
1) First use your calculator to find the zeros of

Now verify the 1 unit integral interval that the zeros are in using the Intermediate Value Theorem.

2) Use the Intermediate Value Theorem to find the 1 unit integral interval for each of the indicated number of zeros.

a) One zero:

2) Use the Intermediate Value Theorem to find the 1 unit integral interval for each of the indicated number of zeros.

b) Four zeros:

3) Given :
• What is a value guaranteed to be between f(2) and f(3).
• What is another value guaranteed to be there?
• What is a value that is NOT guaranteed to be there?