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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

ConceptIncreasing and Decreasing Functions

#### 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

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

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

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

$= 6\left( x - 1 \right)\left( x - 2 \right)$

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

$f'\left( x \right) < 0$

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

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

$\Rightarrow 1 < x < 2$

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

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Solution for 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 concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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