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hpfan101

  • one year ago

Suppose f is continuous on [1,5] and the only solutions of the equation f(x)=6 are x=1 and x=4. If f(2)=8, explain why f(3)>6.

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  1. amistre64
    • one year ago
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    spose we have the same setup, only it is lowered by 6 f(1) = 0, f(4) = 0, f(2) = 2 what does that leave for f(3)? why is f(3)>0 ?

  2. amistre64
    • one year ago
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    think of the intermediate thrm, or whatever it is called ....

  3. hpfan101
    • one year ago
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    f(3) would be greater than 0 because f(1) and f(4) are equal to 0. So f(3) would have to be values between that to satisfy the intermediate value theorem.

  4. hpfan101
    • one year ago
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    Well, that's what I understood from that theorem.

  5. amistre64
    • one year ago
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    yes, f is continuous, and since it has no other f(c)=0 between 1 and 4, then there is noplace or it to cross over at.

  6. amistre64
    • one year ago
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    |dw:1443306445428:dw|

  7. hpfan101
    • one year ago
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    Oh, ok. I understand. Thank you!

  8. amistre64
    • one year ago
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    youre welcome

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