If you are more of a visual person, you should imagine a continuous function, where you know the value of the function at two endpoints, {{MATH_18}} and {{MATH_19}}, but you don't really know what the function does between the points {{MATH_20}} and {{MATH_21}}: {{CMD_22}} {{ENV_23}} {{COMMENT_24}} {{COMMENT_25}} {{COMMENT_26}} {{COMMENT_27}} {{COMMENT_28}} {{CMD_29}} The Intermediate Value Theorem says that despite the fact that you don't really know what the function is doing between the endpoints, a point {{MATH_30}} exists and gives an {{CMD_31}}intermediate value{{CMD_32}} for {{MATH_33}}.