We will concludethis lessonwith a theoremthat will enableus to solvemanypracticalproblemssuchas
findingzerosof functionsand rootsof equations.
IntermediateValue Theorem
If a functionis continuouson a closedinterval then the functionassumeseveryvaluebetweenf(a)
andf(b).
The proofis left as an exercisewith somehintsprovided.(Homework#10).
We can use the IntermediateValue Theoremto analyzeand approximatezerosof functions.
Example3:
Use the IntermediateValue Functionto showthat thereis at leastone zero of the functionin the indicated
interval.
We recallthat the graphof this functionis shapedsomewhatlike a parabola;viewingthe graphin the standard
window, we get the followinggraph: