The function $f (x) = 3 x^{2} + 2 x + 13$ is strictly increasing in the interval

(\frac{1}{3}, \infty)

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(\frac{2}{3}, \infty)

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(- \frac{1}{3}, \infty)

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(- \frac{1}{3}, \frac{1}{3})

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Solution

The correct option is C $(- \frac{1}{3}, \infty)$
$f (x) = 3 x^{2} + 2 x + 13 \Rightarrow f^{'} (x) = 6 x + 2$
For function to be increasing,
$f^{'} (x) > 0 \Rightarrow 6 x + 2 > 0 \Rightarrow x > - \frac{1}{3}$

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