Question

If $f\left(x\right)=\left[x-2\right]$, where $\left[x\right]$ denotes the greatest integer less than or equal to $x$, then $f\text{'}\left(2.5\right)$ is equal to

• A. $\frac{1}{2}$
• B. $0$
• C. $1$
• D. Does not exist.

Answer 1

The correct option is B

$0$

Explanation for the correct option.

Find the value of $f\text{'}\left(2.5\right)$:

For $2\le x<3$ it is seen that $0\le x-2<1$ and so $\left[x-2\right]=0$.

Thus, the function $f\left(x\right)=\left[x-2\right]$ is a constant in the interval $2\le x<3$ and the value of the constant is $0$.

It is known that the derivative of a constant function is zero. So $f\text{'}\left(x\right)=0$ in the interval $2\le x<3$.

As $2.5$ lies in the interval $2\le x<3$ so $f\text{'}\left(2.5\right)=0$.

Thus the value of $f\text{'}\left(2.5\right)$ is $0$.

Hence, the correct option is B.