Verify Rolle's theorem for the function f(x) = x2 - 4x + 3 on [1,… - Vidyadip

Question

Verify Rolle's theorem for the function f(x) = x² - 4x + 3 on [1, 3].

✓

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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