Question

Over what interval is the function differentiable? Y=3/2(x-1)

Answer 1

Answer-

The interval where the function is diffrentiable is

$[-\infty,1)\ \bigcup\ (1,\infty]$

Solution-

The given expression is,

$y=\dfrac{3}{2(x-1)}$

The function will be differentiable where it is continuous and it will not be differentiable, where the function is not continuous.

The function continuous everywhere except at x = 1, because

$\Rightarrow 2(x-1)=0\\\\\Rightarrow x-1=0\\\\\Rightarrow x=1$

at x = 1, its limit does not exist.

Therefore, apart from x=1, this function is differentiable everywhere. The interval will be

$[-\infty,1)\ \bigcup\ (1,\infty]$