Rolle's theorem is not applicable to the function $f(x) = |x|$ defined on $[-1, 1]$ because

The number of values of $C$ that satisfy the conclusion of Rolle's theorem for the function $f(x) = \sin(2 \pi x)$ on the interval $x \in [-1, 1]$ is:

The value of $c$ in the Lagrange's mean value theorem for the function $f(x) = x^{3} - 4x^{2} + 8x + 11$ on the interval $x \in [0, 1]$ is:

For all real values of $a_{0}, a_{1}, a_{2}, a_{3}$ satisfying $a_{0}+\frac{a_{1}}{2}+\frac{a_{2}}{3}+\frac{a_{3}}{4}=0$, the equation $a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}=0$ has a real root in the interval

For the function $f(x) = e^x$ on the interval $[a, b]$ where $a = 0$ and $b = 1$,the value of $c$ in the Lagrange's Mean Value Theorem is:

Verify Rolle's theorem for the function $y=x^{2}+2$ on the interval $[-2, 2]$.