Let f be continuous on [0,1] and suppose that

[kylej]

Let f be continuous on the interval [0, 1] and suppose that 0 < f (x) < 2 for all x on the interval. Show that there is some t in the interval such that f (t) = 3t.

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any help would be greatly appreciated

 

[ksdhart2]

What are your thoughts? What have you tried? As a hint, are you at all familiar with the intermediate value theoremhttps://www.mathsisfun.com/algebra/intermediate-value-theorem.html? Please comply with the rules of the forum as laid out in the Read Before Posting thread that's stickied at the top of every sub-forum and share with us any and all work you've done on this problem, even the parts you know for sure are wrong. Thank you.