Posted by sara on Friday, October 15, 2010 at 10:05pm.
If f is continuous on [1, 1] and f(1) = 4 and f(1) = 3, then there exists a number r such that r < 1 and f(r) = π. Can this be true or false?
Please and thank you

calculus  MathMate, Friday, October 15, 2010 at 10:23pm
The intermediate value theorem states that a function f(x) continuous on the interval [a,b] takes on every value between f(a) and f(b).
In the given case, a=1, b=1, f(a)=4, and f(b)=3. π=3.14159.... lies between 4 and 3.
Therefore the statement "there exists a number r such that r < 1 and f(r) = π" is ______.
See also your previous question:
http://www.jiskha.com/display.cgi?id=1287182780
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