Get live Maths 1-on-1 Classs - Class 6 to 12

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Chapter 6 Class 12 Application of Derivatives

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Last updated at March 16, 2023 by Teachoo

Example 8 Show that the function f given by f (π₯) = π₯3 β 3π₯2 + 4π₯, π₯ β R is strictly increasing on R. f(π₯) = π₯3 β 3π₯2 + 4π₯ Finding fβ(π) fβ(π₯) = 3π₯2 β 3.2π₯ + 4 fβ(π₯) = 3x2 β 6π₯ + 4 fβ(π₯) = 3x2 β 6π₯ + 3 + 1 fβ(π₯) = 3 (π₯2 β 2π₯ + 1) + 1 fβ(π) = 3 (π β 1)2 + 1 As square is a positive number, The value of fβ(π₯) will be always positive for every real number Hence fβ(π) > 0 for all π₯ β R β΄ f(π₯) is strictly increasing