AP Calculus
3.1 – 3.4 Concepts Review
Name ______________________________
1. A _______________ function on a _______________ interval will always
have both a maximum and a minimum value on that interval.
2. The term _______________ value denotes either a maximum or a
minimum value.
3. A critical number of f is a number c such that _______________ or
_______________.
4. If f has a relative minimum or relative maximum at x = c, then c is a
_______________ of f.
5. True or false: If c is a critical number of f, then f has a relative minimum or
a relative maximum at x = c.
6. The Mean Value Theorem says that if f is _______________ on [a, b] and
differentiable on __________, then there is a point c in (a, b) such that
_______________.
7. The function f(x) = |sin x| would satisfy the hypothesis of the Mean Value
Theorem on the interval [0, 1] but would not satisfy them on the interval
[-1, 1] because ________________________________________________.
8. Rolle’s Theorem says if f is _______________ on [a, b] and
_______________ on (a, b) and if _________________, then there is at
least one number c in (a, b) such that _______________.
9. If f‘(x) > 0, then f is _______________; if f“(x) > 0, then f is
____________________.
10. If _______________ and __________ on an open interval I, then f is both
increasing and concave down on I.
11. A point on the graph of a continuous function where the concavity
changes is called a _______________________________.
12. In trying to locate the inflection points for the graph of a function f, we
should look at numbers c, where either _______________ or
_______________.
13. Geometrically, the Mean Value Theorem guarantees the existence on a
______________ line that is parallel to the _______________ line through
(a, f(a)) and (b, f(b)).
14. In terms of rates of change, the Mean Value Theorem implies that there
must be a point in (a, b) at which the _______________ rate of change is
equal to the _______________ rate of change over [a, b].
15. If f‘(c) = 0 and f“(c) > 0, then f(c) is a ______________________________.
16. If f‘(c) = 0 and f“(c) < 0, then f(c) is a ______________________________.
17. If f‘(c) = 0 and f“(c) = 0, then ____________________________________.