4) Let f(x) =12 +4x +x4 a) Find f'(x) b) Find the critical points. c) Construct a sign chart for the first derivative. Then determine the intervals where f(x) is increasing and the intervals where f(x) is decreasing. d) Classify each critical point as a relative maximum/relative minimum or neither. e) Find f"(x) f) Construct a sign chart for the second derivative. Then determine the intervals where f(x) is concave up and the intervals where f(x) is concave down. g) Find the inflection point(s). h) Sketch the graph of f(x)