Find all values of x where the function

Question

f(x)={ x-3 if x ≤ 3

3-x If 3<x<6

^{X^2+5} If 6≤x

is continuous, but not differentiable. List your answers separated by commas.

Answer 1

f(x) is continuous at x = 3 because x - 3 = 3 - x when x = 3. However, f(x) is not differentiable at x = 3 since the graph has a sharp corner when x = 3.

At x = 6, the function is neither continuous nor differentiable because there is a gap in the graph when x = 6.

For all other values of x, the function is both continuous and differentiable.