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Verify Mean Value Theorem, if \( f (x) = x^2 - 4x - 3 \) in the interval \( [a,b]\), where \( a = 1 \) and \(b = 4 \).

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  • $f'(c)=\large\frac{f(b)-f(a)}{b-a}$
Step 1:
It being a polynomial it is continuous in the interval [1,4] and derivable in [1,4].
Step 2:
By Mean Value Theorem we have
We have $f'(c)=2c-4$
answered May 13, 2013 by sreemathi.v

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