Question

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.

Answer 1

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 ?

Answer 2

think of the intermediate thrm, or whatever it is called ....

Answer 3

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.

Answer 4

Well, that's what I understood from that theorem.

Answer 5

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.