### Home > APCALC > Chapter 5 > Lesson 5.1.2 > Problem 5-16

5-16.

Without your graphing calculator, sketch *y* = *f*(*x*) and algebraically determine where the function is increasing, decreasing, concave up, and concave down. List any maxima, minima, and points of inflection. Homework Help ✎

A function is increasing where its first derivative > 0 and decreasing where its first derivative is < 0.

Find these intervals algebraically.

A function is concave up when its second derivative is > 0 and concave down when its second derivative is < 0.

Find these intervals algebraically.

Notice that *x* = 2 is a boundary point. Even though *f* '(2) ≠ 0 and *f* ''(2) ≠ 0, interesting changes in slope and concavity can still happen at *x* = 2.