True or False. If false, give a counter-example.
- If $ f( {-1}) = -1$ and $ f( 1) = 1$, then $ f( 0) = 0$.
- If $ f( {-1})=-1$ and $ f( 1) = 1$, then there is a point $c$, such that
$-1 If $ f( {-1}) = -1, f( 1) = 1$, and $ f( x)$ is continuous, then there
is a point $c$, $ -1 If $ f( 0) = 0, f( 1) =10$ and $ f( x)$ is continuous, then on the
interval $ [0,10], f( x)$ must have a maximum or a minimum value.
- If $ f( x)$ is continuous at a point $a$ then it is differentiable there.
Tags: continuity, IVT, diff, max-min, abstract-function, creating-counterexamples, true-false, t1, c2
One could extend this problem by adding: If true, why is it true?; If false, can you change the statement to make it true?
– James Epperson 1998-08-09