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Ex 6.2, 5 - Find intervals where f(x) = 2x^3 - 3x^2 - 36x + 7 is

Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Ex 6.2, 5 Find the intervals in which the function f given by f (π‘₯) = 2π‘₯3 – 3π‘₯2 – 36π‘₯ + 7 is (a) strictly increasing (b) strictly decreasingf(π‘₯) = 2π‘₯3 – 3π‘₯2 – 36π‘₯ + 7 Calculating f’(𝒙) f’(π‘₯) = 6π‘₯2 – 6π‘₯ – 36 + 0 f’(π‘₯) = 6 (π‘₯2 – π‘₯ – 6 ) f’(π‘₯) = 6(π‘₯^2 – 3π‘₯ + 2π‘₯ – 6) f’(π‘₯) = 6(π‘₯(π‘₯ βˆ’ 3) + 2 (π‘₯ βˆ’ 3)) f’(𝒙) = 6(𝒙 – 3) (𝒙 + 2) Putting f’(x) = 0 6(π‘₯+2)(π‘₯ –3)=0 (π‘₯+2)(π‘₯ –3)=0 So, x = βˆ’2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (βˆ’βˆž ,βˆ’πŸ) & (πŸ‘ ,∞) f is strictly decreasing in (βˆ’πŸ, πŸ‘)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.