Let g(x) be a function such that g(x)>0 for all x, and g′(x)=−g(x) for all x. A function f(x) has derivative f′(x)=(x−3)g(x) for all x. Which one of the following statements is FALSE?

a. f′′(x)=(4−x)g(x)
b. f(x) is increasing on (3,[infinity]).
c. f(x) is concave down on (−[infinity],4).
d. The absolute minimum of f(x) on (−[infinity],[infinity]) occurs at x=3.
e. f(x) has an inflection point at x=4.