Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the
given integers.
-$f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;$ between 1 and 2
A) $f ( 1 ) = 5$ and $f ( 2 ) = - 59$; yes
B) $f ( 1 ) = 5$ and $f ( 2 ) = 59$; no
C) $f ( 1 ) = - 5$ and $f ( 2 ) = - 59$; no
D) $f ( 1 ) = - 5$ and $f ( 2 ) = 59$; yes

Question

Quizplus · Accepted Answer

The Intermediate Value Theorem states that if a function $f$ is continuous on a closed interval $[a, b]$ and $N$ is any number between $f(a)$ and $f(b)$, then there exists at least one number $c$ in the interval $[a, b]$ such that $f(c) = N$. Calculating $f(1) = -3(1)^4 - 4(1)^3 + 9(1) + 3 = 5$ and $f(2) = -3(2)^4 - 4(2)^3 + 9(2) + 3 = -59$, we see that the function values change signs from positive to negative between 1 and 2, indicating there is at least one real zero in that interval.

Use the Intermediate Value Theorem to Determine Whether the Polynomial f(x)=−3x4−4x3+9x+3;f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;f(x)=−3x4−4x3+9x+3;

Use the Intermediate Value Theorem to Determine Whether the Polynomial $f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;$