Example 8 - Chapter 6 Class 12 Application of Derivatives
Last updated at August 2, 2026 by Teachoo
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Chapter 6 Class 12 Application of Derivatives
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Example 8 Show that the function f given by f (š„) = š„3 ā 3š„2 + 4š„, š„ ā R is strictly increasing on R. f(š„) = š„3 ā 3š„2 + 4š„ Finding fā(š) fā(š„) = 3š„2 ā 3.2š„ + 4 fā(š„) = 3x2 ā 6š„ + 4 fā(š„) = 3x2 ā 6š„ + 3 + 1 fā(š„) = 3 (š„2 ā 2š„ + 1) + 1 fā(š) = 3 (š ā 1)2 + 1 As square is a positive number, The value of fā(š„) will be always positive for every real number Hence fā(š) > 0 for all š„ ā R ā“ f(š„) is strictly increasing
