Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = 4 x ^ { 3 } + 2 x - 7 ; 1$ and 2
A) $f ( 1 ) = 1$ and $f ( 2 ) = 29$
B) $f ( 1 ) = 0$ and $f ( 2 ) = 30$
C) $f ( 1 ) = 1$ and $f ( 2 ) = - 29$
D) $f ( 1 ) = - 1$ and $f ( 2 ) = 29$

Question

Quizplus · Accepted Answer

The intermediate value theorem states that if a continuous function changes sign over an interval, it must have a zero in that interval. Here, $f(1) = -1$ and $f(2) = 29$, so the function changes sign between 1 and 2, indicating a real zero exists in that interval.

Use the Intermediate Value Theorem for Polynomials to Show That f(x)=4x3+2x−7;1f ( x ) = 4 x ^ { 3 } + 2 x - 7 ; 1f(x)=4x3+2x−7;1

Use the Intermediate Value Theorem for Polynomials to Show That $f ( x ) = 4 x ^ { 3 } + 2 x - 7 ; 1$