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
$\frac{1}{2}$
D
$\text{dose not exist}$

✓

Answer

$\text{dose not exist}$

Solution:

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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