Question

Rolle’s theorem is not applicable to function ƒ(x) = |x| in the interval [-3, 3] because –

• A. ƒ is continuous in (–3, 3)
• B. ƒ(3) = ƒ(–3)
• C. ƒ(x) ³ 0 for x in [-3, 3]
• D. ƒ is not derivable in (–3, 3)

Answer 1

Answer: (D)

ƒ is not derivable in (–3, 3)

Answer 2

Here, ƒ ¢ (x) = $\frac{x}{|x|}$which does not exist at

0 Ī (–3, 3) Hence, Rolle’s theorem is not applicable to

ƒ(x) in [–3, 3] as ƒ is not derivable in (–3, 3).