Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be
determined, indicate so.
-$f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 8 \text { in } [ - 1,4 ]$
A)Cannot determine
B)Yes

Question

Quizplus · Accepted Answer

The Boundedness Theorem states that if a function is continuous on a closed interval, then it is bounded on that interval. The given function $f(x) = x^4 - 3x^3 + 5x^2 - 9x - 8$ is a polynomial, and polynomials are continuous everywhere, including on the interval $[-1, 4]$. Therefore, the zeros of $f(x)$ are bounded over the given interval.

Use the Boundedness Theorem to Determine If the Zeros of F(x)are