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Verify Rolle's theorem for the following function; $f(x)=x^{2}, 0\leq x\leq 1$

Note: This is part 2nd of a 4 part question, split as 4 separate questions here.

1 Answer

  • Rolle's Theorem: Let $f$ be a real valued function that satisfies the following conditions:
  • (i) f is defined and continuous on the closed interval $[a,b]$
  • (ii) f is differentiable in the open interval $(a,b)$
  • (iii) $f(a)=f(b)$
  • Then there exists at least one value $c \in (a,b)$ such that $f'(c)=0$
$f(x)=x^2 \qquad 0 \leq x \leq 1$
$f(x)$ being a polynomial function . It is continuous in [-1,1], differentiable in (-1,1)
$f(0)=0 \qquad f(1)=1$
The conditions for Rolle's theorem are not satisfied.
answered Jul 24, 2013 by meena.p