Chapter 4.3, Problem 98E

(a)

To determine

Whether the function f is concave down and positive everywhere, if f is continuous on $\left(-\infty ,\infty \right)$, if it is possible then give an example, if it is not then give explanation.

(b)

To determine

Whether a function f that increases and is concave down everywhere where f is continuous on $\left(-\infty ,\infty \right)$. If it is possible, then give an example and if not, then give explanation.

(c)

To determine

Whether a function f has exactly two local extreme and three inflection points. If it is possible, then give an example and if not, then give an explanation.

(d)

To determine

Whether a function f has exactly four zeros and two local extreme is possible. If yes, then give an example, else give an explanation.