Find the intervals in which the function $f$ given by $f(x)=2x^2− 3x$ is (a) strictly increasing (b) strictly decreasing

The correct answer is (a) strictly increasing in interval $(\dfrac{3}{4},∞)$
(b) strictly decreasing in the interval $(−∞,\dfrac{3}{4})$

$f(x)=2x^2− 3x$


Differentiate $f'(x)=4x−3$


$f'(x)=0 ⇒ 0=4x−3 ⇒ x=\dfrac{3}{4}$




The point $x=2$ divides the curve into two disjoint intervals namely $(−∞,\dfrac{3}{4})$ and $(\dfrac{3}{4},∞)$



In the interval $(−∞,\dfrac{3}{4})$, $f'(x)=4x−3<0$


Hence, $f$ is strictly decreasing in $(−∞,\dfrac{3}{4})$



In the interval $(\dfrac{3}{4},∞)$, $f'(x)>0$


Hence, in the interval $(\dfrac{3}{4},∞)$, the function $f$ is strictly increasing.