Question

Concavity: Determine whether the following properties can be satisfied by a function that is continuous on (-inf,inf). If such a function is possible, provide an example 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 threee inflection points.
d. A function f has exactly four zeros and two local extrema.

Answer 1

a. Would be a square function that opens down and does not cross the x-axis sort of like -x^2 - 1