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# Find the intervals in which the function f given by f (x) = 2 x^2 - 3 x is increasing

4. Find the intervals in which the function f given by $f ( x) = 2x ^2 - 3 x$ is  (a) increasing

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$f ( x) = 2x ^2 - 3 x$
$f^{'}(x) = 4x - 3$
Now,
$f^{'}(x) = 0$
4x - 3 = 0
$x = \frac{3}{4}$

So, the range is  $\left ( -\infty, \frac{3}{4} \right ) \ and \ \left ( \frac{3}{4}, \infty \right )$
So,
$f(x)< 0$   when  $x \ \epsilon \left ( -\infty,\frac{3}{4} \right )$        Hence, f(x) is strictly decreasing in this range
and
$f(x) > 0$     when  $x \epsilon \left ( \frac{3}{4},\infty \right )$             Hence, f(x) is strictly increasing in this range
Hence, $f ( x) = 2x ^2 - 3 x$   is strictly increasing in   $x \epsilon \left ( \frac{3}{4},\infty \right )$

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