Intermediate Value Theorem...3

Calculus
Section 2.5







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it is the Lambert W-function

x=- (2W0(e^(3/2)/2)-3)/2
Decimal: x=0.59420 => which is between -2 and 1,718

here is more about Lambert W-function

https://mathworld.wolfram.com/LambertW-Function.html

 

You said the Lambert x-value in decimal form is 0.59420, which lies between f(0) and f(1). However, 0.59420 is not between the given open interval
(0, 1). I don't think x = 0.59420 is the answer.

You say?

 

0< 0.59420<1, so x = 0.59420 is the answer

 

You are right. We are seeking for a solution that lies between the given interval not between f(0) and f(1). Overall, this is not too bad. I don't understand the importance of this theorem. However, I do like the fact that it becomes straightforward after solving a few problems.