Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given
integers
-$f ( x ) = 5 x ^ { 3 } - 7 x + 7$; between $- 2$ and $- 1$
A) $f ( - 2 ) = 19$ and $f ( - 1 ) = - 9$; yes
B) $f ( - 2 ) = - 19$ and $f ( - 1 ) = 9$; yes
C) $f ( - 2 ) = 19$ and $f ( - 1 ) = 9$; no
D) $f ( - 2 ) = - 19$ and $f ( - 1 ) = - 9$; no

Question

Quizplus · Accepted Answer

The Intermediate Value Theorem states that if a continuous function changes sign over an interval, there is at least one real zero in that interval. Since $f(-2) = -19$ and $f(-1) = 9$, the function changes sign, indicating a real zero between $-2$ and $-1$.

Use the Intermediate Value Theorem to Determine Whether the Polynomial f(x)=5x3−7x+7f ( x ) = 5 x ^ { 3 } - 7 x + 7f(x)=5x3−7x+7

Use the Intermediate Value Theorem to Determine Whether the Polynomial $f ( x ) = 5 x ^ { 3 } - 7 x + 7$