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Question
Verify Rolle's theorem for the following function on the indicated interval f (x) = log (x2 + 2) − log 3 on [−1, 1] ?
Solution
The given function is \[f\left( x \right) = \log\left( x^2 + 2 \right) - \log3\] ,which can be rewritten as
\[ \Rightarrow f'\left( x \right) = \frac{3\left( 2x \right)}{x^2 + 2} = \frac{6x}{x^2 + 2}\]
\[ \Rightarrow \frac{6x}{x^2 + 2} = 0\]
\[ \Rightarrow x = 0\]
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