Question

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

• A. $\left( - \frac{1}{4},0 \right)$
• B. (0, 2)
• C. (–∞, –1)
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

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

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

⇒ x ∈ $\left( - \frac{1}{4},0 \right)$ ∪ $\left( \frac{1}{4},\infty \right)$