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Choose the correct option from the given alternatives : Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in ______.

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Question

Choose the correct option from the given alternatives :

Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in ______.

Options

  • `(-oo, 1)`

  • `[3, oo)`

  • `(-oo, 1] ∪ [3, oo)`

  • (1, 3)

MCQ
Fill in the Blanks
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Solution

Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in (1, 3).

Explanation:

Here, `f(x) = 3x^2 - 12x + 9`

= `3(x - 1)(x - 3) ≤ 0 ⇔ x ∈ [1, 3]`

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Chapter 2: Applications of Derivatives - Miscellaneous Exercise 1 [Page 92]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 2 Applications of Derivatives
Miscellaneous Exercise 1 | Q 5 | Page 92

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