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Question
f (x) = 2x2 − 5x + 3 on [1, 3] Discuss the applicability of Rolle's theorem for the following function on the indicated intervals ?
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Solution
The given function is \[f\left( x \right) = 2 x^2 - 5x + 3\] on \[\left[ 1, 3 \right]\] .
The domain of f is given to be \[\left[ 1, 3 \right]\] .
It is a polynomial function.
Thus, it is everywhere derivable and hence continuous.
But
\[f\left( 1 \right) = 0 \text { and }f\left( 3 \right) = 6\]
\[ \Rightarrow f\left( 3 \right) \neq f\left( 1 \right)\]
Hence, Rolle's theorem is not applicable for the given function.
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