Find the intervals in which the function $f$ given by $f(x) = 2{x^2} - 3x$ is

(a) strictly increasing

(b) strictly decreasing

We have, $f(x) = d - 3x$ …(i)
$f(x)$ is a polynomial function. Hence, $f(x)$ is continuous and derivable on $R$.

Differentiating (i) w.r.t. $x$, we get $f(x) = 4x - 3.$

(a) For strictly increasing,
$f'(x) > 0 \Rightarrow 4x - 3 > 0 \Rightarrow x > \cfrac{3}{4}$
Therefore, $f$ is strictly increasing on $\left( {\cfrac{3}{4},\infty } \right)$

(b) For strictly decreasing
$f'(x) < 0 \Rightarrow 4x - 3 < 0 \Rightarrow x < \cfrac{3}{4}$
Therefore, $f$ is strictly decreasing on $\left( { - \infty ,\;\cfrac{3}{4}} \right)$