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Suppose that 2 ≤ f '(x) ≤ 4 for all values of x. What are the minimum and maximum...

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sllysmith | Student, Undergraduate | (Level 2) eNoter

Posted April 5, 2012 at 2:43 PM via web

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Suppose that 2 ≤ f '(x) ≤ 4 for all values of x. What are the minimum and maximum possible values of

f(5) − f(3)?

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cosinusix | College Teacher | (Level 3) Assistant Educator

Posted April 6, 2012 at 3:43 AM (Answer #1)

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Integrate the given inequalities between 3 and 5.

 

`int_3^5 2dxlt=int_3^5f'(x)dxlt=int_3^5 4d x`

 

`4lt=f(5)-f(3)lt=8 `

 

f(5)-f(3) is between 4 and 8.

 f(5)-f(3) can be 4 is f'(x) is constant, equal to 2

f(5)-f(3) can be 8 is f'(x) is constant equal to 4

Therefore the minimum possible value of f(5)-f(3) is 4.

The maximum possible value of f(5)-f(3) is 8.

 

 

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