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Chap4_Sec3

# Chap4_Sec3 - Increasing Decreasing TEST Example 1(4.3 Find...

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Find where the function f ( x ) = 3 x 4 – 4 x 3 – 12 x 2 + 5 is increasing and where it is decreasing. f’ ( x ) = 12 x 3 - 12 x 2 - 24 x = 12 x ( x – 2)( x + 1) Example 1 (4.3) Increasing/ Decreasing TEST

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The graph of f confirms the information in the chart. Example 1 I/D TEST
WHAT DOES f’ SAY ABOUT f ? Find the local minimum and maximum values of the function f in Example 1. Example 2 (4.3)

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WHAT DOES f’ SAY ABOUT f ? Find the local maximum and minimum values of the function g ( x ) = x + 2 sin x 0 x 2 π Example 3 (4.3)
WHAT DOES f’ SAY ABOUT f ? As g is differentiable everywhere, the only critical numbers are 2 π /3 and 4 π /3. So, we analyze g in the following table. The graph of g supports our conclusion. Example 3

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The figure shows a population graph for Cyprian honeybees raised in an apiary. square4 How does the rate of population increase change over time? square4 When is this rate highest? square4 Over what intervals is P concave upward or concave downward?
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Chap4_Sec3 - Increasing Decreasing TEST Example 1(4.3 Find...

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