Rolles Theorem The function is differentiable on and satisfies However, its derivative
Chapter 4, Problem 63(choose chapter or problem)
Rolle’s Theorem The function
\(f(x)=\left\{\begin{array}{ll}0, & x=0 \\1-x, & 0<x \leq 1\end{array}\right.\)
is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is never zero on (0. 1). Does this contradict Rolle's Theorem? Explain.
Text Transcription:
f(x)={0, x=0
1-x, 0 < x leq 1
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