Which is the strongest correct statement about differentiability and continuity at a point?

A function $g$ is continuous at $x=5$. What follows about $g^{\prime }(5)$?

A student writes: $v^{\prime }(4)$ exists, so $v$ is continuous at $x=4$. Which best evaluates this argument?

A function $q$ is differentiable at $x=-7$ and $q(-7)=7$. Which conclusion is guaranteed?

Use the graph of $k$. What follows about $k^{\prime }(2)$?

A student writes: $u$ is differentiable at $x=-8$ and its graph is smooth there, so $u^{\prime }(-8)=0$. Which best evaluates this argument?

Which statement is the CONTRAPOSITIVE of "if $f$ is differentiable at $a$, then $f$ is continuous at $a$"?

A function $s$ is differentiable at $x=-7$ and $s(-7)=-2$. Which conclusion is guaranteed?

Which statement is true for every function $f$ and every point $a$ in its domain?

Which function shows that a function can be continuous at a point without being differentiable there?

A function $r$ is differentiable at $x=2$ and $r(2)=3$. Which conclusion is guaranteed?

Which function shows that a function can be continuous at a point without being differentiable there?

For how many points can a function be continuous but not differentiable?

A function $r$ is differentiable at $x=-4$ and $r(-4)=9$. Which conclusion is guaranteed?

A function $s$ is differentiable at $x=6$ and $s(6)=-8$. Which conclusion is guaranteed?

Use the graph of $s$. A student writes: $s^{\prime }(-6)$ does not exist, so $s$ must be discontinuous at $x=-6$. Which best evaluates this argument?

Which function shows that a function can be continuous at a point without being differentiable there?

Which function shows that a function can be continuous at a point without being differentiable there?

A student writes: $s^{\prime }(9)$ does not exist, so $s$ must be discontinuous at $x=9$. Which best evaluates this argument?

Use the graph of $w$. A student writes: $w^{\prime }(4)$ does not exist, so $w$ must be discontinuous at $x=4$. Which best evaluates this argument?