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.