Q107 / 160 · AP EAMCET 2024 (23 May Shift 1) · Mathematics

In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange's mean value theorem is not applicable

  • A
    $f(x)=|x| ; 1 \leq x \leq 5$
  • B
    $f(x)=[x],[\sqrt{2}, \sqrt{3}]$
  • Correct answer
    C
    $f(x)=\log \left(x^2-1\right),\left[\frac{1}{e}, e-2\right]$
  • D
    $f(x)=e^x ;[-e, e]$

Solution

$f(x)=\log \left(x^2-1\right), x \in\left[\frac{1}{e}, e-2\right]$ $f\left(\frac{1}{e}\right)$ does not exist $\Rightarrow f(x)$ is not continuous on $\left[\frac{1}{e}, e-2\right]$ $\therefore$ Lagrange's mean value theorem is not applicable.

Hence, the correct answer is option: 'C'.

Relevant Questions