Question

Number of point(s) in $[1,2]$ where $f(x)=(-2{)}^{\left[x^3\right]}$ is non-differentiable (where $[.]$ denotes greatest integer function)

Answer 1

Answer: 7

$1\le x^3\le 8$
discontinuous at $x^3=2,3,4,5,6,7$; hence non differentiable
$f(1)=-2$
$f(1+h)=-2$ continuous and differentiable at
$x=1$
$f(8)=(-2{)}^{8^3}\&f(2-h)$
$=\underset{h\to 0}{\lim }(-2{)}^{[(8-h)]}=(-2{)}^7$
Non-differentiable for $x^3=8$
Total points of non-differentiablity are $7$ .