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Derivative increasing without bounds

  • Thread starter apiwowar
  • Start date
  • #1
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if f'(x) > 0 for all real values of x then x increases without bounds. I thought that was true but in the back of the book it says false and uses f(x)=2x/sqrt(x2+2) as an example. i worked out the derivative and got f'(x) = 4/(x2+2)3/2.

how does that show that the first sentence is false? i'm quite confused abou this
 

Answers and Replies

  • #2
Dick
Science Advisor
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You got the derivative right. And it's always positive, yes. But f(x) doesn't increase without bound. It approaches 2 as x->inf. Can you show that?
 
  • #3
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asymptotes :D
 

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