Consider the function f(x) = sqrt(x^2+1).

(a) Find the intervals where f(x) is increasing, and the intervals where it is decreasing.

(b) Find the intervals where f(x) is concave up, and the intervals where it is concave down, and determine the x-values of any inflection points.

(c) Find the absolute maximum and absolute minimum values of f(x), if they exist, and say where each occurs. If either does not exist, explain why.

(d) Sketch a graph of y = f(x) below (for the x-values shown).

4 2 -3 -2 -1 0 2 3 -2