If f(x)=(x−1)(x−2) and interval given was (0,4), find 'c' using Langrange's mean value theorem.
A
2+2√3
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B
2−2√3
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C
2
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D
Both A and B
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Solution
The correct option is C2 Here f(x)=(x−1)(x−2). Now f(x) is continuous on [0,4] and differentiable on (0,4). Thus applying LMVT, we get f(4)−f(0)4−0=f′(c) ⇒6−24=c−2+c−1 ⇒1=2c−3 ⇒c=2