If S is the interval such that f(x) = 8x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

If S is the interval such that f(x) = 8x² – ln |x| increases in S then S contains

Options:

$(-\frac{1}{4},0)$

(0, 2)

(-∞, -1)

none of these

Correct Answer:

$(-\frac{1}{4},0)$

Explanation:

Here $f'(x)= 16 x-\frac{1}{x} =\frac{16}{x}(x^2-\frac{1}{16})$.

For an increasing function, $f'(x)>0⇒\frac{1}{x}(x-\frac{1}{4})(x+\frac{1}{4})>0$.

Hence (A) is the correct answer.