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Ex 5.8, 2 - Examine if Rolle’s theorem - Chapter 5 Class 12 - Ex 5.8

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Examine if Rolle’s theorem is applicable to the functions. Can you say some thing about the converse of Rolle’s theorem from this function? (𝑖) 𝑓 (𝑥) = [𝑥] 𝑓𝑜𝑟 𝑥 ∈ [5, 9] Greatest Integer less than equal to 𝑥 𝑓 (𝑥) =[𝑥] is not continuous & differentiable ⇒ Condition of Rolle’s Theorem is not satisfied. Therefore, Rolle’s Theorem is not applicable . Ex 5.8, 2 Examine if Rolle’s theorem is applicable to the functions. Can you say some thing about the converse of Rolle’s theorem from this function? (𝑖𝑖) 𝑓 (𝑥) = [𝑥] 𝑓𝑜𝑟 𝑥 ∈ [−2, 2] Greatest Integer less than equal to 𝑥 𝑓 (𝑥) =[𝑥] is not continuous & differentiable ⇒ Condition of Rolle’s Theorem is not satisfied. Therefore, Rolle’s Theorem is not applicable . Ex 5.8, 2 Examine if Rolle’s theorem is applicable to the functions. Can you say some thing about the converse of Rolle’s theorem from this function? (𝑖𝑖𝑖) 𝑓 (𝑥) = 𝑥2 – 1 𝑓𝑜𝑟 𝑥 ∈ [1, 2]

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