Consider the following in respect of the function $f(x)=10^x$ : 1. Its domain is $(-\infty, \infty)$ 2. It is a continuous function 3. It is differentiable at $x=0$ Which of the above statements are correct?

• A

  1 and 2 only
• B

  2 and 3 only
• C

  1 and 3 only
• Correct answer
  D

  1, 2 and 3

Solution

It is clear from function that domain $=(-\infty, \infty)$ and it is continuous function unique tangant can be drawn at $\mathrm{x}=0$ so, it is differentiable at $\mathrm{x}=0$

Hence, the correct answer is option: 'D'.