Go back to the definition: g(x) is differentiable at 0 if exists. So, does that limit exist, or not?
Suppose that f(x) is any function that is continuous at x=0.
Prove that the function g(x) = xf(x) is differentiable at x=0.
Now my first instinct was to say that this cannot be done.
If a function is continuous at a certain value of x does not mean its differentiable at that point as well.
Can someone shed some light here.
Maybe the question intends for the function to be differentiable at (x) as well.