Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) f(x) = (sqrt x + 5 ) + 5

Question

I don't understand

Answer 1

I'm assuming you meant f(x) = √(x + 5) + 5

Think of the graph. The function will be differentiable, as long as the graph has no sharp points/corners, no holes, no jumps, or no vertical asymptotes or vertical sections.

Here is the graph:

Can you see that there is a sharp "endpoint" at x = -5 (the beginning of the graph)? The derivative will not be defined there. There is also no derivative to the left of that (there is no graph there).

So the function is differentiable on (-5, ∞)