Given f(x)=x^5-4x-1, find an interval of length no more than 1 where there must be a zero

Question

Calculus 1 question about intervals

Answer 1

f(x) = x^5 - 4x -1 . Clear that f(-1)= (-1)^5 - 4(-1)-1 = 2>0, f(0) = -1<0.

By Intermediate Value Theorem iinterval (-1,0) contains at least one real zero of given polinomial f(x).

Length of this interval is 1.

Answer 2

Hi Matt,

f(1) and f(2) are negative and positive, respectively. The Intermediate Value Theorem tells you about a value in between.