Use calculus to find any critical points and inflection points of the given function. Then determine the concavity of the function and the intervals over which it is increasing/decreasing.
f(x) = e-2x
◦ Critical points: none
Inflection points: point of inflection at x = 0
Concavity: concave down for all x < 0 and concave up for all x > 0
Decreasing: decreasing for all real numbers
◦ Critical points: critical point at x = 0
Inflection points: none
Concavity: concave up for all real numbers
Increasing: increasing for all x < 0 and decreasing for all x > 0
◦ Critical points: none
Inflection points: none
Concavity: concave down for all real numbers
Decreasing: decreasing for all real numbers
◦ Critical points: none
Inflection points: none
Concavity: concave up for all real numbers
Decreasing: decreasing for all real numbers
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