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anonymous

  • 5 years ago

1. Differentiable functions are always continuous. 2. If f(x)=e2, then f(x)=2e. 3. If f(c)=0 and f(c)0, then f(x) has a local minimum at c. 4. If f(x) and g(x) are increasing on an interval I, then f(x)g(x) is increasing on I. 5. A continuous function on a closed interval always attains a maximum and a minimum value. 6. If f(c)=0, then c is either a local maximum or a local minimum. 7. If f(x)0 for all x in (0,1), then f(x) is decreasing on (0,1).

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  1. anonymous
    • 5 years ago
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    Any thoughts?

  2. anonymous
    • 5 years ago
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    t f t t t t f

  3. anonymous
    • 5 years ago
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    I think some of the formatting on these is off.

  4. anonymous
    • 5 years ago
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    For example: 2. If f(x)=e2, then f(x)=2e. What does that mean?

  5. anonymous
    • 5 years ago
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    it's missing some stuff on my question thou: 2. If f(x)=e2, then f ' (x)=2e. 3. If f ' (c)=0 and f ' ' (c)>0, then f(x) has a local minimum at c. 7. If f ' (x)<0 for all x in (0,1), then f(x) is decreasing on (0,1)

  6. anonymous
    • 5 years ago
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  7. anonymous
    • 5 years ago
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    Well then I disagree with your answers for 7, 6

  8. anonymous
    • 5 years ago
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    err 6 and 7 rather.

  9. anonymous
    • 5 years ago
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    is 6 not true?

  10. anonymous
    • 5 years ago
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    No. Look at the derivative of \(x^3\). The derivative equals 0 at x=0, but the function is strictly increasing for all x, so it has no local mins/maxes.

  11. anonymous
    • 5 years ago
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    x=0 is an inflection point.

  12. anonymous
    • 5 years ago
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    ooh i see

  13. anonymous
    • 5 years ago
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    The derivative must be 0 and the concavity must not change signs to have a min/max

  14. anonymous
    • 5 years ago
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    yea otherwise it's just an inflection point.

  15. anonymous
    • 5 years ago
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    indeed

  16. anonymous
    • 5 years ago
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    if the 2nd derivative is >0 then there is a min, right?

  17. anonymous
    • 5 years ago
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    I think so yes. The concavity will be positive and not changing signs

  18. anonymous
    • 5 years ago
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    yea C.U. has min's Differentiable functions are always continuous - this one false cause they're not always cont. right ?

  19. anonymous
    • 5 years ago
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    Differentiable functions are always continuous I think. But the reverse is not true, continuous functions are not always differentiable.

  20. anonymous
    • 5 years ago
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    I have to head home. If you have more questions I'll check back later.

  21. anonymous
    • 5 years ago
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    alright thanks

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