190
Chapter 2 | Limits
Solution No. The Intermediate Value Theorem only allows us to conclude that we can find a value between f (0) and f (2); it doesn’t allow us to conclude that we can’t find other values. To see this more clearly, consider the function f ( x ) = ( x −1) 2 . It satisfies f (0) =1>0, f (2) =1>0, and f (1) =0.
Example 2.38 When Can You Apply the Intermediate Value Theorem?
For f ( x ) =1/ x , f (−1) =−1<0 and f (1) =1>0. Can we conclude that f ( x ) has a zero in the interval [−1, 1]?
Solution No. The function is not continuous over [−1, 1]. The Intermediate Value Theorem does not apply here.
Show that f ( x ) = x 3 − x 2 −3 x +1 has a zero over the interval [0, 1].
2.26
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online