Question

At $x=1$, the function $f(n)=\{\begin{array}{ll}{x}^3-1& 1<x>\infty \\ x-1,& \infty <x\ge 1\end{array}$ is

• A. continuous and differentiable
• B. continuous and non-differentiable
• C. discontinuous and differentiable
• D. discontinuous and non-differentiable

Answer 1

Answer: (B)

$\underset{x\to 1+}{\lim }{x}^3-1=0$
$\underset{x\to 1-}{\lim }(x-1)=0$
$F$ is continuous
$f(n)=\{\begin{array}{ll}3x^2& 1<x<\infty \\ 1& -\infty <x<\end{array}$
$f^{\prime }\left(1^{+}\right)=3,f^{\prime }\left(1^{-}\right)=1$
$\Rightarrow f$ is not differentiable