Consider the function f(x) = e (x² + 1). (a) Given that f'(x) = e² (x² + 2x + 1), determine the interval(s) on which ƒ is increasing and on which f is decreasing. (b) Given that f"(x) = e²(x² +4x+3), determine the intervals on which ƒ is concave up and on which ƒ is concave down. (c) For each of i) the 1st Derivative Test and ii) the 2nd Derivative Test, can the test be used to determine whether f has any relative extrema? If so, what is the result of the test? If not, explain why.

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