What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for 1 < x < 3?(a) Decreases(b) Increases(c) Cannot be determined for 1 < x < 3(d) A constant functionI had been asked this question during a job interview.This key question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12

What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for 1 < x <

1.	What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for 1 < x < 3?(a) Decreases(b) Increases(c) Cannot be determined for 1 < x < 3(d) A constant functionI had been asked this question during a job interview.This key question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12
Answer» Correct choice is (B) Increases 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 1 < 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 1 < x < 3 So, f(x) increases for VALUES of 1 < x < 3.

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