1. Chapter 5 Class 12 Continuity and Differentiability
2. Serial order wise

Transcript

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]

Serial order wise

About the Author

Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.