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Example 11 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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Example 11 Find the intervals in which the function f given by f (đĽ)=4đĽ3â6đĽ2 â72đĽ+30 is (a) strictly increasing (b) strictly decreasing. f (đĽ)=4đĽ3â6đĽ2 â72đĽ+30 Calculating fâ(x) f (đĽ)=4đĽ3â6đĽ2â72đĽ+30 đâ˛(đĽ)=12đĽ2â12đĽ â72đĽ đâ˛(đĽ) =12(đĽ2âđĽ â 6) đâ˛(đĽ) =12(đĽ2â3đĽ+2đĽ â6) đâ˛(đĽ) = 12(đĽ(đĽ â 3) + 2(đĽ â 3)) đâ˛(đ)=đđ(đ+đ)(đ âđ) Putting fâ(x) = 0 12(đĽ+2)(đĽ â3)=0 (đĽ+2)(đĽ â3)=0 So, x = â2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (ââ ,âđ) & (đ ,â) f is strictly decreasing in (âđ, đ)
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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