Question

Find the intervals in which the function $f$ given by $f\left(x\right)=2x^2-3x$ is

$\left(a\right)$ increasing
$\left(b\right)$ decreasing

Answer 1

$f\left(x\right)=2x^2-3x$
Differentiating w.r.t $x,$

$f^{\prime }\left(x\right)=4x-3$
Putting $f^{\prime }\left(x\right)=0$

$4x-3=0$

$\Rightarrow x=\frac{3}{4}$

Plotting point on number line,

Intervals	Sign of $f^{\prime }\left(x\right)$
$(-\infty ,\frac{3}{4})$	$<0$
$(\frac{3}{4},\infty )$	$>0$

Hence, (a) increasing in

$(\frac{3}{4},\infty )$

(b) decreasing in

$(-\infty \frac{3}{4})$