Question

If `f(x) = (x^n - a^n)/(x - a)` for some constant, a, then f'(a) is equal to ______.

Options

• 1

• 0

• does not exist

• `1/2`

Answer 1

If `f(x) = (x^n - a^n)/(x - a)` for some constant, a, then f'(a) is equal to does not exist.

Explanation:

Given `f(x) = (x^n - a^n)/(x - a)`

`f"'"(x) = ((x - a)(n * x^(n - 1)) - (x^n - a^n) * 1)/(x - a)^2`

∴ `f""(a) = ((a - a)(n * a^(n - 1)) - (a^n - a^n))/(a - a)^2`

So `f"""(a) = 0/0`

= does not exist