hpfan101
  • hpfan101
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.
Calculus1
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
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 ?
amistre64
  • amistre64
think of the intermediate thrm, or whatever it is called ....
hpfan101
  • hpfan101
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.

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hpfan101
  • hpfan101
Well, that's what I understood from that theorem.
amistre64
  • amistre64
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.
amistre64
  • amistre64
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hpfan101
  • hpfan101
Oh, ok. I understand. Thank you!
amistre64
  • amistre64
youre welcome

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