Determine whether the following properties can be satisfied by a function that is continuous on (-∞, ∞). If such a function is possible, provide an example or a sketch of the function. If such a function is not possible, explain why.

a. A function f is concave down and positive everywhere.

b. A function f is increasing and concave down everywhere.

c. A function f has exactly two local extrema and three inflection points.

d. A function f has exactly four zeros and two local extrema.