Increasing/Decreasing; Minimums/Maximums Unit 2 (2.2 Polynomial Functions)

Increasing/Decreasing;

Minimums/MaximumsUnit 2 (2.2 Polynomial Functions)

Warm-UpW/O a calculator, describe the end

behavior Use your calculator to:

Determine the zeros and their multiplicity

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Objectives

Students will be able to find the minimums and maximums of a polynomial using the calculator

Students will be able to identify the intervals on which the graph of a polynomial is increasing and/or decreasing

Students will be able to graph a polynomial (using the LCT, zeros and mins/maxs)


Relative Maximum and Minimum Values


x

y

x

y

Relative minimum

Relative maximum

Approximate the relative minimum of thefunction:


– 6

– 6

6

6

Zoom In:

– 0.86– 4.79

– 1.79

2.14

Zoom In:

0.58 0.76

-3.24

-3.43

The approximate minimum is (0.67, –3.33).


Press: 2nd Calc 3:minimum Left Bound? Right Bound? Guess?

Find the exact value of the relative minimum of

TI-84

The exact value is (0.67, –3.33).

Practice


Find the exact value of the relative minimum or maximum of

Increasing and Decreasing


Increasing – When the graph is growing or going up

Decreasing – When the graph is falling or going down

**Always in terms of the x values! Written in interval notation (x-values!)

The graph of y = f (x):


Increases on _____________

Decreases on ______________

Increases on ______________ (3, – 4)

x

y(–3, 6)

–2

2

Practice Problems


Graph the following functions and determine the zeros, the max and mins and where it is increasing and decreasing

Working Backwards


Write the equation of least degree with the following roots:

1. 3, 4, -2

2. -1, 7, 2i, -2i

3. 0 multiplicity 3, 4, 2 multiplicity 2.

Closure


Graph the function by applying the LCT (determine end behavior), and finding the zeros (all w/o a calc)

Then state the mins/maxs and the intervals on which the graph is increasing/decreasing

Classwork/Homework

Worksheet (Graphing Polynomials)Review tomorrowQuiz Monday!! (on Graphing

Polynomials)


Increasing/Decreasing; Minimums/Maximums Unit 2 (2.2 Polynomial Functions)

Documents

Transcript of Increasing/Decreasing; Minimums/Maximums Unit 2 (2.2 Polynomial Functions)