AP Calculus Unit 5

0.0(0)
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Get a hint
Hint

Rolle’s Theorem

Get a hint
Hint

If f is continuous + differentiable, and f(a) = f(b), then there is a point, c, where f’( c) = 0

Get a hint
Hint

Mean Value Theorem

Get a hint
Hint

If f is continuous + differentiable, then there is a point, c, where f’( c) = (f(b) - f(a)) / (b - a) (inst r.o.c = avg r.o.c)

Card Sorting

1/8

Anonymous user
Anonymous user
flashcard set

Earn XP

Description and Tags

test thurs-fri jan 11-12

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

9 Terms

1
New cards

Rolle’s Theorem

If f is continuous + differentiable, and f(a) = f(b), then there is a point, c, where f’( c) = 0

2
New cards

Mean Value Theorem

If f is continuous + differentiable, then there is a point, c, where f’( c) = (f(b) - f(a)) / (b - a) (inst r.o.c = avg r.o.c)

3
New cards

Extreme Value Theorem

If f is continuous on [a,b], then f has both an extreme maximum and minimum on [a,b]

4
New cards

Critical Numbers

Where f’( c) = 0 or DNE

5
New cards

First Derivative Test

c is a critical number

If f’(x) goes from neg to pos at c, then f( c) is a relative minimum

If f’(x) goes from pos to neg at c, then f( c) is a relative maximum

6
New cards

Canditate Test

Used for finding absolute extrema

  1. Evaluate f at each critical number in (a,b)

  2. Evaluate f at each endpoint of [a,b]

7
New cards

Test for Concavity

If f’(x) > 0 for all x in (a,b), then f is concave up on (a,b)

If f’(x) < 0 for all x in (a,b), then f is concave down on (a,b)

8
New cards

Point of Inflection

Where a graph changes concavity; either f’ ’(x) = 0 or f’(x) DNE

9
New cards

Second Derivative Test

Used for finding relative max or mins. f’( c) = 0

  1. If f ‘ ‘( c) > 0, then f( c) is a relative minimum

  2. If f ‘ ‘( c) < 0, then f( c) is a relative maximum

  3. If f’ ‘( c) = 0, refer to First Derivative Test