Intermediate value theorem
Limits and continuity · Mathematics
Study notes
Q: Show x³ − x − 1 = 0 has a root between 1 and 2. f(1) = −1 < 0, f(2) = 5 > 0. f continuous (polynomial). By IVT, some c in (1,2) has f(c) = 0. (Bisection: try 1.5: f = 0.875 > 0, so root in (1,1.5).)