### Home > CALC3RD > Chapter Ch5 > Lesson 5.1.2 > Problem 5-16

5-16.

Without your graphing calculator, sketch and algebraically determine where the function is increasing, decreasing, concave up, and concave down. List any maxima, minima, and points of inflection.

A function is increasing where its first derivative

Find these intervals algebraically.

A function is concave up when its second derivative is

Find these intervals algebraically.

Notice that is a boundary point. Even though

*and*

*, interesting changes in slope and concavity can still happen at*

*.*