What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for x < 1?(a) Decreases(b) Increases(c) Cannot be determined for x < 1(d) A constant functionThis question was posed to me by my college director while I was bunking the class.Query is from Calculus Application topic in division Application of Calculus of Mathematics – Class 12

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

1.	What will be nature of the f(x) = 10 – 9x + 6x^2 – x^3 for x < 1?(a) Decreases(b) Increases(c) Cannot be determined for x < 1(d) A constant functionThis question was posed to me by my college director while I was bunking the class.Query is from Calculus Application topic in division Application of Calculus of Mathematics – Class 12
Answer» Correct answer 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 < 1, 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 < 1 So, f(x) decreases for values of x < 1.

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