Question

Identify the point at which f(x) is not differentiable

Answer 1

Answer:

$\large \boxed{\sf \ \ \text{Answer B. } \ \ x = 2 \ \ }$

Step-by-step explanation:

Hello, we can write that

$f(x)=(x-2)^{\dfrac{2}{3}}=e^{\dfrac{2}{3}ln(x-2)} \ \text{ where e is the exponential function. }$

The ln() function is not differentiable in 0, meaning when x - 2 = 0, which gives x=2 (add 2 in both parts of the equation).

This is why f is not differentiable in x = 2.

Hope this helps.

Thank you