### Home > APCALC > Chapter 8 > Lesson 8.2.2 > Problem8-82

8-82.

Multiple Choice: The maximum value of $f(x) = x(x - 3)(x - 7)$ over the interval $0 ≤ x ≤ 7$ is nearest to:

1. $8$

1. $12$

1. $14$

1. $16$

1. $22$

Expand f before differentiating.

Remember that a maximum value is a y-value, not an x-value.

Notice that this is a CLOSED domain: $0 ≤ x ≤ 7$.
Since maxima can exist where $f '(x) = 0$ or where $f^\prime(x) = \text{ DNE}$, it is important to check the y-values at each endpoint.
$f(0) =$________ and $f(7) =$ ________
After all, an endpoint might exceed the y-values where $f ^\prime(x) = 0$; in which case, that endpoint will be in the global maximum.