CBSE Class 12 Sample Paper for 2025 Boards

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Question 36 (iii) (B) - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Oct. 3, 2024 by

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Question 36 (iii) (B) Check whether V has a point of inflection at π‘₯=65/6 or not?Now, 𝐕(𝐱) = 2(2π‘₯^3βˆ’65π‘₯^2+500π‘₯) 𝐕′(𝐱) = 4(π‘₯βˆ’5)(3π‘₯βˆ’50) 𝐕^β€²β€² (𝐱) = 4 (6π‘₯βˆ’65) Now, for point of inflection… it is not necessary for V’(x) to be zero But, V’’(x) = 0 is important And, Sign of V’’(x) on left and right of the point should change At 𝒙=πŸ”πŸ“/πŸ” 𝑽^β€²β€² (πŸ”πŸ“/πŸ”) = 4 (6 Γ—65/6βˆ’65) = 4 (65βˆ’65) = 0 Now, Checking Sign of V’’(x) on left and right of 𝒙=πŸ”πŸ“/πŸ” Since V’’(65/6) = 0 And, Sign of V’’(x) on left and right of π‘₯=65/6 changes Thus, x = πŸ”πŸ“/πŸ” is a point of inflection

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo