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Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R. - Mathematics and Statistics

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प्रश्न

Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.

बेरीज
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उत्तर

f(x) = x3 – 6x2 + 12x – 16

∴ f'(x) = `"d"/"dx" ("x"^3 - "6x"^2 + "12x" - 16)`

= 3x2 – 6 × 2x + 12 × 1 – 0
= 3x2 – 12x + 12
= 3(x2 – 4x + 4)
= 3(x - 2)2 ≥ 0 for all x ∈ R
∴ f'(x) ≥ 0 for all x ∈ R
∴ f is increasing for all x ∈ R.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Applications of Derivatives - Exercise 2.4 [पृष्ठ ८९]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 2 Applications of Derivatives
Exercise 2.4 | Q 1.1 | पृष्ठ ८९
बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 4 Applications of Derivatives
Exercise 4.2 | Q 1.1 | पृष्ठ १०६

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