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The function f(x) = 2x2-1x4, x > 0, decreases in the interval ______.

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Question

The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.

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Solution

The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval `(1, oo)`.

Explanation:

We have f(x) = `(2x^2 - 1)/x^4`

f'(x) = `(x^4(4x) - (2x^2 - 1) * 4x^3)/x^8`

⇒ f'(x) = `(4x^5 - (2x^2 - 1) * 4x^3)/x^8`

= `(4x^3[x^2 - 2x^2 + 1])/x^8`

= `(4(-x^2 + 1))/x^5`

For decreasing the function f'(x) < 0

∴ `(4(-x^2 + 1))/x^5 < 0`

⇒  `-x^2 + 1 < 0`

⇒ x2 < 1

∴ x > ± 1

⇒  `x ∈ (1, oo)`

Hence, the required interval is `(1, oo)`

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Chapter 6: Application Of Derivatives - Exercise [Page 142]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 6 Application Of Derivatives
Exercise | Q 63 | Page 142

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