To work this problem, he uses the definition of the limit.
View Intermediate Value Theorem Images. The intermediate value theorem states that if a continuous function attains two values, it must also attain all values in between these two values. When we have two points connected by a continuous curve here is the intermediate value theorem stated more formally
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An arbitrary horizontal line (green) intersects the function. If f is a continuous function over a,b, then it takes on every value between f(a) and f(b) over that interval. This example shows how the intermediate value theorem only ensures output values between f(a) and f(b) even though there are more values outside this part of the range.
To answer this question, we need to know what the intermediate value theorem says.
At some point within the interval. A typical argument using the ivt is: When we have two points connected by a continuous curve here is the intermediate value theorem stated more formally Your teacher probably told you that you can draw the graph of a continuous function without lifting your pencil off the paper.
