What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for x > 3?(a) Decreases(b) Increases(c) Cannot be determined for x > 3(d) A constant functionThe question was posed to me during an online exam.I'd like to ask this question from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12

What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for x > 3?(

1.	What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for x > 3?(a) Decreases(b) Increases(c) Cannot be determined for x > 3(d) A constant functionThe question was posed to me during an online exam.I'd like to ask this question from Calculus Application topic in portion Application of Calculus of Mathematics – Class 12
Answer» The CORRECT OPTION is (a) Decreases For explanation: f(x) = 10 – 9x + 6x^2 – x^3 Thus, f’(x) =– 9 + 12X –3 x^2 = -3(x^2 – 4x + 3) Or f’(x) = -3(x – 1)(x – 3) ……….(1) If x > 3, then x – 1 > 0 and x – 3 > 0 Hence, (x – 1)(x – 3) > 0 Thus, from (1) it readily follows that, f’(x) < 0, when x > 3 So, f(x) decreases for VALUES of x > 3.

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