Question

Consider the following statements:
$1.$ Derivative of $f\left(x\right)$ may not exist at some point.
$2.$ Derivative of $f\left(x\right)$ may exist finitely at some point.
$3.$ Derivative of $f\left(x\right)$ may be infinite (geometrically) at some point.
Which of the above statements are correct?

• A. $1$ and $2$ only
• B. $2$ and $3$ only
• C. $1$ and $3$ only
• D. $1,2$ and $3$

Answer 1

Answer: (D)

$1,2$ and $3$

Lets check each statement one by one

1. This statement is true. Take example $y=|x|$ derivative does not exist at $x=0$

2. This statement is true. Derivative may be finite may be not. Take example of $y=\tan x$

3. Derivative of a function can be infinite(undefined)

Hence, all three statements are true.