Column – Ι Column – ΙΙ [16JM120179]
, x ∈ [0, π ] (p) Conditions in Rolle's theorem are satisfied.
(q) Conditions in LMVT are satisfied.
(s) At least one condition in LMVT is not satisfied
Text Solution
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f(x) is continuous and differentiable f(0) = f( π )
Hence condition in Rolle ’ s theorem and LMVT are satisfied.
f(1 – ) = – 1, f(1) = 0, f(1 + ) = 1
f(x) is not continuous at x = 1, belonging to 
Hence, atleast one condition in LMVT and Rolle ’ s theorem is not satisfied
f ’ (x) = 
(x – 1) – 3/5 , x ≠ 1
At x = 1, f(x) is not differentiable.
Hence at least one condition in LMVT and Rolle ’ s theorem is not satisfied.
At x = 0
L.H.D. = 
= 
= – 1
R.H.D. = 1
At x = 0, f(x) is not differentiable
Hence at least one condition in LMVT and Rolle ’ s theorem is not satisfied.
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