AP EAMCET · Maths · Application of Derivatives
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 \(f(x)=[x],[\sqrt{2}, \sqrt{3}]\)
- C \(f(x)=\log \left(x^2-1\right),\left[\frac{1}{e}, e-2\right]\)
- D \(f(x)=e^x ;[-e, e]\)
Answer & Solution
Correct Answer
(C) \(f(x)=\log \left(x^2-1\right),\left[\frac{1}{e}, e-2\right]\)
Step-by-step Solution
Detailed explanation
\(f(x)=\log \left(x^2-1\right), x \in\left[\frac{1}{e}, e-2\right]\) \(f\left(\frac{1}{e}\right)\) 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.
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