The function \[ f(x)=\left\{\begin{array}{ll} x^{4}+x^{2}-x+2 & \te...

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The function
\[
f(x)=\left\{\begin{array}{ll}
x^{4}+x^{2}-x+2 & \text { for } x \leq 1 \\
3 x^{3}-x^{2}+x & \text { for } x1
\end{array}\right.
\]
is
(a) continuous everywhere
(b) differentiable everywhere
(c) not differentiable at \( x=1 \)
(d) such that \( f^{\prime} \) exists everywhere but \( f^{\prime \prime} \) is not continuous at \( x=1 \).
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