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) = 6 - e-x

Question

A. Critical points: critical point at x = 0
Inflection points: none
Concavity: concave down for all real numbers 
Increasing: increasing for all x < 0 and decreasing for all x > 0
B. Critical points: none
Inflection points: none
Concavity: concave up for all real numbers
Decreasing: decreasing for all real numbers
C. 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 
Increasing: increasing for all real numbers
D. Critical points: none
Inflection points: none
Concavity: concave down for all real numbers
Increasing: increasing for all real numbers

Answer 1

Answer: D