Question

If [t] denotes the greatest integer $\le t$, then number of points, at which the function $f(x)=4|2x+3|+9\left[x+\frac{1}{2}\right]-12[x+20]$ is not differentiable in the open interval $(-20,20)$, is

Answer 1

Answer: 79

$f(x)=4|2x+3|+9\left[x+\frac{1}{2}\right]-12[x+20]$
$x\in (-20,20)$
$f(x)$ is not Diff. at
$x=I\in \{-19,-18,\dots .0,\dots 19\}=39$
at $x=I+\frac{1}{2},f(x)$ Non diff. at 39 points
Check at $x=\frac{-3}{2}$ Discount at $x=\frac{-3}{2}$
$\therefore$ N. R(1)
No. of point of non-differentiabilty
$=39+39+1=79$