Provide an Appropriate Response Is Never Zero

question 240

Essay

Provide an appropriate response.
- $\text { The function } f ( x ) = \left\{ \begin{array} { l l } 2 x & 0 \leq x < 1 \\0 & x = 1\end{array} \text { is zero at } x = 0 \text { and } x = 1 \text { and differentiable on } ( 0,1 ) \text {, but its derivative on ( } 0,1 \right)$ is never zero. Does th is example contradict Rolle's Theorem?

---

Definitions:

Masculine Prowess

A term often associated with the demonstration of traditionally male qualities and physical abilities, especially strength and aggression.

College Binge Drinking

The consumption of an excessive amount of alcohol in a short period, often associated with college or university students.

Secondhand Effects

Negative consequences experienced by individuals as a result of others' behaviors, such as being harmed by a drunk driver or living with someone who smokes.

Binge Drinking

The consumption of an excessive amount of alcohol in a short period of time, with the intention of becoming intoxicated.