In the mean value theorem, $f(b) - f(a) = (b - a)f'(c)$if $a = 4$, $b = 9$ and $f(x) = \sqrt x $ then the value of  $c$  is

  • A

    $1 - {{\sqrt {15} } \over 6}$

  • B

    $1 + \sqrt {15} $

  • C

    $1 - {{\sqrt {21} } \over 6}$

  • D

    $1 + \sqrt {21} $

Similar Questions

For the function$x + {1 \over x},x \in [1,\,3]$, the value of $ c$  for the mean value theorem is

Rolle's theorem is not applicable to the function $f(x) = |x|$ defined on $ [-1, 1] $ because

In which of the following functions Rolle’s theorem is applicable ?

Let $a > 0$ and $f$ be continuous in $[- a, a]$. Suppose that $f ' (x) $ exists and $f ' (x) \le 1$ for all $x \in (- a, a)$. If $f (a) = a$ and $f (- a) = - a$ then $f (0)$

The function $f(x) = {(x - 3)^2}$ satisfies all the conditions of mean value theorem in $[3, 4].$ A point on $y = {(x - 3)^2}$, where the tangent is parallel to the chord joining $ (3, 0)$  and $(4, 1)$  is