Method: Intermediate Value Theorem

Step 1: Confirm that the given equation is continuous on the given x-interval .

This normally does not require you to do any actual calculation, as it is not really a simple process to show an entire x-interval is continuous. It is really just you doing a mental check on the equation, and stating that the equation is continuous on the given x-interval so that someone grading knows you considered it.

Step 2: Plug the interval endpoint x-values , $[a,b]$, into the given equation to identify your y-value interval.

These are the y-values that you know you will get every y-values in between. If it is a real-world model, you will usually need to identify those end points from the language of the problem.

Step 3: Draw you conclusion based on the Intermediate Value Theorem.