Question $23$

$1$ pts

Evaluate the function for the given values of a and $b.$ Then use the intermediate value theorem to determine which of the statements below is true.

$a=-1$ and $b=0$

$f(x)=5x^3+4x+2$

$f(-1)$ and $f(0)$ have opposite signs, therefore $f$ does not have a real zero between $-1$ and $0.$

$f(-1)$ and $f(0)$ have the same sign, therefore $f$ does not have a real zero between $-1$ and $0.$

$f(-1)$ and $f(0)$ have opposite signs, therefore $f$ has a real zero between $-1$ and $0.$

$f(-1)$ and $f(0)$ have the same sign, therefore the intermediate value theorem cannot be used to determine whether f has a real zero between $-1$ and $0.$