In each part, determine whether all of the hypotheses of theMean-Value Theorem are
Chapter 4, Problem 76(choose chapter or problem)
In each part, determine whether all of the hypotheses of the Mean-Value Theorem are satisfied on the stated interval. If not, state which hypotheses fail; if so, find all values of \(c\) guaranteed in the conclusion of the theorem.
(a) \(f(x)=|x-1|\) on \([-2,2]\)
(b) \(f(x)=\frac{x+1}{x-1}\) on \([2,3]\)
(c) \(f(x)=\left\{\begin{array}{lll}3-x^{2} & \text { if } & x \leq 1 \\2 / x & \text { if } & x>1\end{array}\right.\) on \([0,2]\)
Equation Transcription:
on
on
{
on
Text Transcription:
c
f(x)=|x-1| on [-2,2]
f(x)=x + 1/x - 1 on [2,3]
f(x)={ _2/x if x > 1 ^3-x^2 if x leq 1 on [0,2]
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