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find the average rate of change of over the interval (0,9 ]

Find The Average Rate Of Change Of Over The Interval 09 class=

Sagot :

Semsee45idn

Answer:

3.  10/9

4.  34

Step-by-step explanation:

The average rate of change of f(x) over the interval a ≤ x ≤ b is:

[tex]\sf \dfrac{f(b)-f(a)}{b-a}[/tex]

Problem 3

Given interval: 0 ≤ x ≤ 9

From inspection of the graph:

  • f(0) = -7
  • f(9) = 3

[tex]\sf average \ rate \ of \ change=\dfrac{f(9)-f(0)}{9-0}=\dfrac{3-(-7)}{9}=\dfrac{10}{9}[/tex]

Problem 4

Given:

  • function f(x) = x³ - 9x
  • interval: 1 ≤ x ≤ 6

⇒ f(1) = (1)³ - 9(1) = -8

⇒ f(6) = (6)³ - 9(6) = 162

[tex]\sf average \ rate \ of \ change=\dfrac{f(6)-f(1)}{6-1}=\dfrac{162-(-8)}{5}=34[/tex]

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