Intermediate Value Theorem...4

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Calculus
Section 2.5

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MSP412224fc6h909b31hhe00002238dceh15f25i28
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:

112_mean_value_theorem.png


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

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