Verify Rolle's theorem for the function f(x) = x^2 - 4x + 3 on [1… - Vidyadip

Question

Verify Rolle's theorem for the function $f(x) = x^2 - 4x + 3$ on $[1, 3].$

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Answer

$f (x)$ being a polynomial is continuous in $[1, 3]$ and differentiable in $(1, 3).$
Also $f (a) = f (1) = 0 = f (b) = f (3)$
$\therefore$ Roll's Theorem is applicable
$\Rightarrow\text{f '(c)}=2\text{c} - 4 = 0 $
$\Rightarrow\text{c}=2\in(1, 3)$
Hence Rolle's theorem is verified.

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