Ex 6.2, 18 - Prove that f(x) = x3 - 3x2 + 3x - 100 is increasing - To show increasing/decreasing in whole domain

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Ex 6.2,18 Prove that the function given by f ( ) = 3 3 2 + 3 100 is increasing in R. f = 3 3 2 + 3 100 We need to show f is strictly increasing on R i.e. we need to show f > 0 Finding f f = 3x2 6x + 3 0 = 3 2 2 +1 = 3 2+ 1 2 2 1 = 3 1 2 f = 3 1 2 We know that Square of any number is always + ve 1 2 > 0 3 1 2>0 f > 0 Hence f > 0 for any value of f is strictly increasing on R

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