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Last updated at April 16, 2024 by Teachoo

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)