Question

The value of c in Lagrange's theorem for the function $f\left(x\right)=|x|$ in the interval [-1, 1] is

• A. $0$
• B. $1/2$
• C. $-1/2$
• D. non-existent in the interval

Answer 1

Answer: (D)

non-existent in the interval

$f\left(x\right)=|x|$ in the interval [-1, 1] is
Since, |x| is not differentiable at $x=0$
So, Lagrange theorem is not applicable to f(x) in [-1, 1].
Hence, no value of 'c' exists.