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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat 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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