Question

If $f\left(x\right)=\left(x - 1\right)\left(x - 2\right)\left(x - 3\right)\left(x - 4\right)\left(x - 5\right)$ , then the value of $\left(\text{f}\right)^{'} \left(5\right)$ is equal to

• A. $0$
• B. $120$
• C. $24$
• D. $5$

Answer 1

Answer: (C)

$\left(\text{f}\right)^{'} \left(\text{x}\right) = \left(\text{x} - 2\right) \left(\text{x} - 3\right) \left(\text{x} - 4\right) \left(\text{x} - 5\right) + \left(\text{x} - 1\right) \left(\text{x} - 3\right) \left(\text{x} - 4\right) \left(\text{x} - 5\right)$
$+......+\left(x - 1\right)\left(x - 2\right)\left(x - 3\right)\left(x - 4\right)$
Putting $x=5$ , we get,
$\left(\text{f}\right)^{'} \left(5\right) = 0 + 0 + 0 + 0 + \left(5 - 1\right) \left(5 - 2\right) \left(5 - 3\right) \left(5 - 4\right)$
$\left(\text{f}\right)^{'} \left(5\right) = 24$