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Examine the applicability of Mean Value Theorem for all three functions given in $(iii)\;f (x) = x^2-1 \;for\; x \: \in [1,2]$

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  • By Mean value theorem $f'(c)=\large\frac{f(b)-f(a)}{b-a}$
Step 1:
$f(x)=x^2-1$ for $x\in [1,2]$
It is polynomial.Therefore it is continuous in the interval [1,2].
Step 2:
$c=\large\frac{3}{2}$ which belongs to $(1,2)$
answered May 14, 2013 by sreemathi.v

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