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Solution for Function F(X) = 2x3 − 9x2 + 12x + 29 is Monotonically Decreasing When (A) X < 2 (B) X > 2 (C) X > 3 (D) 1 < X < 2 - CBSE (Science) Class 12 - Mathematics

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Question

Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
(a) x < 2
(b) x > 2
(c) x > 3
(d) 1 < x < 2

Solution

(d) 1 < x < 2

\[f\left( x \right) = 2 x^3 - 9 x^2 + 12x + 29\]

\[f'\left( x \right) = 6 x^2 - 18x + 12\]

\[ = 6 \left( x^2 - 3x + 2 \right)\]

\[ = 6\left( x - 1 \right)\left( x - 2 \right)\]

\[\text { For f(x) to be decreasing, we must have }\]

\[f'\left( x \right) < 0\]

\[ \Rightarrow 6\left( x - 1 \right)\left( x - 2 \right) < 0 \]

\[ \Rightarrow \left( x - 1 \right)\left( x - 2 \right) < 0 \left[ \text { Since }6 > 0, 6\left( x - 1 \right)\left( x - 2 \right) < 0 \Rightarrow \left( x - 1 \right)\left( x - 2 \right) < 0 \right]\]

\[ \Rightarrow 1 < x < 2\]

\[\text { So,f(x) is decreasing for }1 < x < 2 .\]

  Is there an error in this question or solution?
Solution Function F(X) = 2x3 − 9x2 + 12x + 29 is Monotonically Decreasing When (A) X < 2 (B) X > 2 (C) X > 3 (D) 1 < X < 2 Concept: Increasing and Decreasing Functions.
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