If $f$ is continuous for $axb$ and differentiable for $f^{\text{'}}(c)=\frac{f(b)-f(a)}{b-a}c{f}^{\text{'}}(c)=0$cfa$x$bfa$xb{\displaystyle \underset{a}{\overset{b}{}}}f(x)dxa.$

$(C)f$ has a minimum value $onaxb.$

$(D)f$ has a maximum value $onaxb.$

$(E){\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$ exists.$a.$

$(B)f^{\text{'}}(c)=0$ for some $c$ such that $a.$

$(C)f$ has a minimum value $onaxb.$

$(D)f$ has a maximum value $onaxb.$

$(E){\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$ exists.$a,$ which $of$ the following could $be$ false?

$(A)f^{\text{'}}(c)=\frac{f(b)-f(a)}{b-a}$ for some $c$ such that $a.$

$(B)f^{\text{'}}(c)=0$ for some $c$ such that $a.$

$(C)f$ has a minimum value $onaxb.$

$(D)f$ has a maximum value $onaxb.$

$(E){\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$ exists.