(Steps Shown) Verify that f satisfies the conditions of Rolle’s Theorem on the indicated interval and find all numbers c on the interval such that f '(c)=0.


Question: Verify that f satisfies the conditions of Rolle’s Theorem on the indicated interval and find all numbers c

on the interval such that f '(c)=0.

  1. \(f\left( x \right)={{x}^{4}}-{{x}^{3}},\,\,\,\left[ 0,1 \right]\)
  2. \(f\left( x \right)=2\sin \left( \frac{1}{2x} \right),\,\,\,\left[ 0,\pi \right]\)

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