examday

/TMUA

The function $f(x)$ is continuous and defined for all real $x$. Which of the following conditions is/are sufficient for the function to have exactly one root $x$ in the interval $x\in[-1,1]$?

• I. $f(-1)=-67$, $f(2)=67$, and $f'(x)>0$ for $x\in[-1,1]$
• II. $f(-2)=67$, $f(1)=-67$, and $f'(x)<0$ for all $x$
• III. $f(-1)=-67$, $f(1)=67$