No, the function has a sharp turn the first quadrant, so it is not option C(yellow).
What is a continuous function?
A continuous function is one where the graph has no breaks, jumps, or holes. It can be drawn without lifting the pen, exhibiting a smooth and connected behavior.
In the graph of the function
The function is not differentiable for all x-values because it has a sharp turning the first quadrant, so it is not differentiable.
The presence of the sharp turn prevents the smooth connection of the curve.
There is no smooth transition along the length of the curve.
So, no, the function has a sharp turn the first quadrant, so it is not differentiable is the correct option C(yellow).