What do you know about the derivative? What about the possible intervals on which the function is increasing and decreasing?

There are infinitely many such functions. For simplicity, we'll choose a simple polynomial.1b) What is a possible function that fits these characteristics?

Our polynomial must have a continuous derivative, so Thus, for some constant . We have to choose a negative value for in order for the derivative to be positive and negative in the appropriate intervals, so we'll take . Now, integrate and make an arbitrary choice for the integration constant to get a suitable .