MCQ

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If $\text{f(x)}=|\log_{10}\text{x}|\text{fx}=\log_{10}\text{x},$ then at $x = 1:$

1. $f(x)$ is continuous and $\text{f}\ '(1^+)=\log_{10}\text{e}$
2. $f(x)$ is continuous and $\text{f}\ '(1^+)=\log_{10}\text{e}$
3. $f(x)$ is continuous and $\text{f}\ '(1^-)=-\log_{10}\text{e}$
4. $f(x)$ is continuous and $\text{f}\ '(1^-)=-\log_{10}\text{e}$

• A
  $a$ and $b$
• B
  $a$ and $c$
• C
  $b$ and $c$
• ✓
  $a$ and $d$