Intermediate Value Theorem...4

Calculus
Section 2.5

 

as you can see, x=0 lies between -1.0907 and 0.841471

 

Yes, I keep forgetting that we are looking for a solution to the equation in the given interval. In fact, x = 0 and x is approximately 1.61755 both lie between 1 and 2 but NOT BETWEEN f(1) and f(2).

You say?

Additional Question:

What is so important about the Intermediate Value Theorem? In what way is this theorem important in the real world? Is this just another theorem for classroom use only?

 

notes:



Recall that (f(b)-f(a))/(b-a) is slope of line through points (a,f(a)) and (b,f(b)).

 

Did we cover the Mean Value Theorem? I don't think so. What's the importance of both theorems?

 

no, we did

https://www.math-forums.com/threads/intermediate-value-theorem.442596/

The mean value theorem is not the same as the intermediate value theorem. The mean value theorem is all about the differentiable functions and derivatives, whereas the intermediate theorem is about the continuous function.

 

Your graph here reads Mean Value Theorem. See other?