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CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3]$
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Answer

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

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