20.5k views
2 votes
Suppose f(x) = x³ - 6x + 1. Does the Intermediate Value Theorem guarantee that f(x) will have a root on the interval (2, 3)? Answer yes or no in the answer box in D2L and put your work and answer with explanation on your paper.

1 Answer

2 votes

Answer:

Yes (see below for explanation

Explanation:


f(2)=2^3-6(2)+1=8-12+1=-4+1=-3\\f(3)=3^3-6(3)+1=27-18+1=9+1=10

Therefore, since
f(2) < 0 < f(3), then the Intermediate Value Theorem guarantees that
f(x) will have a root on the interval
(2,3).

User Javorosas
by
7.8k points

Related questions

asked Mar 26, 2024 177k views
ELLIOTTCABLE asked Mar 26, 2024
by ELLIOTTCABLE
8.4k points
1 answer
4 votes
177k views
1 answer
5 votes
181k views
1 answer
5 votes
33.2k views