Question

Rolle's theorem is not applicable to the function f(x) = |x| defined on [–1, 1] because
[AISSE 1986; MP PET 1994, 95]

• A.
  f is not continuous on [ –1, 1]
• B. f is not differentiable on (–1,1)
• C. $f(-1)\ne f\left(1\right)$
• D. $f(-1)=f\left(1\right)\ne 0$

Answer 1

The correct option is B

f is not differentiable on (–1,1)

Rolle's theorem is not applicable to the function f(x) = |x| defined on [–1, 1] because f(x) = |x| is not differntiable in (-1,1).
f(x) = |x| is not differentiabe at x = 0. It has a sharp point at x = 0.