solve B&C please

2. [10 points. To demonstrate that polynomial interpolation is ill-behaved for some functions f(x), consider this classical example: $(2) = 1 +252 on (a, b) = (-1,1). (a) 'Show' that f(x) is infinitely often differentiable. Idea: Compute the first few derivatives, then argue. What is the domain of f(a) and of its derivatives? This shows that the error formula for interpolation applies. However, will the derivatives of f(x) be uniformly bounded as n oo, that is, is there one number 0