For which interval, function {{{x^2} - 3x} over {x - 1}} satisfies all conditions of Rolle's the

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5. Continuity and Differentiation

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For which interval, the function ${{{x^2} - 3x} \over {x - 1}}$ satisfies all the conditions of Rolle's theorem

A

$[0, 3]$

B

$[-3, 0]$

C

$[1.5, 3]$

D

For no interval

Solution

(d) Here $f(x) = \frac{{{x^2} – 3x}}{{x – 1}}$

==>$f'(x) = \frac{{x^2 -2x +3}}{{{(x-1)}^2}}$

Obviously, it is not derivable at $x = 1$ $i.e.,$ in $(0,3)$

Also $f(a) = f(b)$ does not hold for $[ – 3,\,0]$ and $ [1. 5, 3]$

Hence the answer is $ (d)$

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