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: