TRUE OR FALSE:

$($i$)6.$ If $f(x)$ is a continuous function defined on the closed interval $-4,-1$ and $f(-4)=1$ and $f(-1)=-5,$ then the equation $f(x)=0$ must have at least one solution in the interval $(-4,-1).$

$($i$)7.$ If $f(x)$ is a continuous function defined on the closed interval $-7,-2$ and $f(-7)=-2$ and $f(-2)=-6,$ then there must be some $c$ in $(-7,-2)$ such that $f(c)=\frac{-30}{7}.$

$($i$)8.$ If $f(x)$ is an arbitrary function defined on the closed interval $5,12$ and $f(5)=-3$ and $f(12)=-2,$ then there must be som $c$ in $(5,12)$ such that $f(c)=\frac{-17}{7}.$