If f(x)= x^n-a^n x-a , then f'(a) is : - Vidyadip

MCQ

If $\text{f(x)}=\frac{\text{x}^\text{n}-\text{a}^\text{n}}{\text{x}-\text{a}},$ then $\text{f}'\text{(a)}$ is :

A
$1$
B
$0$
C
$\frac{1}{2}$
✓
$\text{dose not exist}$

✓

Answer

Correct option: D.

$\text{dose not exist}$

Given : $\text{f(x)}=\frac{\text{x}^\text{n}-\text{a}^\text{n}}{\text{x}-\text{a}}$
Now $, f(x)$ is not difined at $x = a.$
Therefore $, f(x)$ is not differentiable at $x = a.$
So $, f\ '(a)$ dose not exist.
Hence, the correct answer is option $(d).$

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