Chapter 3.1, Problem 1C

a)

To determine

Whether Rolle’s Theorem is a special case of Mean Value Theorem.

b)

To determine

Whether the statement “Mean Value Theorem is so named as it signify the average rate of change of a function on an interval” is true or false.

c)

To determine

Whether the statement “If $f$ is differentiable on $ℝ$ and has an extremum at $x=-2$ then $f\text{'}(-2)=0$ ” is true or false.

d)

To determine

Whether the statement “If $f$ has a critical point at $x=1$ then $f$ has a local maximum or local minimum at $x=1$ ” is true or false.

e)

To determine

Whether the statement “ $f$ is any function such that $f(2)=0$ and $f(8)=0$ then there is some $c$ in the interval $(2,8)$ such that $f\text{'}(c)=0$ ” is true or false.

f)

To determine

Whether the statement “ $f$ is any continuous and differentiable function such that $f(-2)=4$ and $f(2)=0$ then there is some $c$ in the interval $\left(-2,2\right)$ such that $f\text{'}(c)=-1$ ” is true or false.

g)

To determine

Whether the statement is true or false.

To determine

Whether the statement “ f is continuous and differentiable on [0,10] and $f\text{'}(5)=0$ ” is true or false.