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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