$f (x) = | 3 x - 4 |$ has least value at $x =$

\frac{3}{4}

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\frac{4}{3}

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Solution

The correct option is A $\frac{4}{3}$
$f (x) = ⎧ ⎨ ⎩ \begin{matrix} 3 x - 4 & I f x > \frac{4}{3} - (3 x - 4) & I f x < \frac{4}{3} \end{matrix}$
$f^{'} (x) = ⎧ ⎨ ⎩ \begin{matrix} 3 & I f x > \frac{4}{3} - 3 & I f x < \frac{4}{3} \end{matrix}$
$f (x)$ is minimum at $x = \frac{4}{3}$

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