I'm stuck on a homework question from my high school calculus course.
Is f(x)=x|x| differentiable at x=0?
I know what the graph of f(x) looks like based on Geometer's Sketchpad. I also know that a function is differentiable at a point if the derivative at that point exists.
Does the derivative at x=0 exist? Is the function differentiable?
Since it's an absolute value function, wouldn't the derivative be f '(x)= -2x when x<0 and f '(x)= 2x when x>0? Is there an equation for the derivative at zero?