Intuitive proof of the Intermediate value theorem to first year calculus students I want to give an informal proof of the intermediate value theorem to my calculus students. They have just learned about continuity and they don't know yet about derivatives among more other advanced topics.
Do you think it's possible?

Assume that $f(a)<c<f(b)$, bisect the interval $[a,b]$ into $[a_{2},b_{2}]$ such that $f(a_{2})<c<f(b_{2})$ (if this fails, that means we have reached the goal). Proceed this again to get $[a_{3},b_{3}]$... so the left endpoints and right endpoints converge to a point $\eta$, continuity then implies $f(\eta)=c$. 
