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Unit: Applying derivatives to analyze functions
AP Calc:
FUN (BI)
, FUN‑1 (EU)
, FUN‑4 (EU)
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About this unit
The first and the second derivative of a function give us all sorts of useful information about that function's behavior. The first derivative tells us where a function increases or decreases or has a maximum or minimum value; the second derivative tells us where a function is concave up or down and where it has inflection points.AP Calc:
FUN (BI)
, FUN‑1 (EU)
, FUN‑1.B (LO)
, FUN‑1.B.1 (EK)
Learn
Practice
- Using the mean value theoremGet 3 of 4 questions to level up!
- Justification with the mean value theoremGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑1 (EU)
, FUN‑1.C (LO)
, FUN‑1.C.1 (EK)
, FUN‑1.C.2 (EK)
, FUN‑1.C.3 (EK)
Learn
Practice
- Find critical pointsGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.1 (EK)
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.2 (EK)
Learn
Practice
- Relative minima & maximaGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.3 (EK)
Learn
Practice
- Absolute minima & maxima (closed intervals)Get 3 of 4 questions to level up!
- Absolute minima & maxima (entire domain)Get 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.4 (EK)
, FUN‑4.A.5 (EK)
Learn
Practice
- Concavity introGet 3 of 4 questions to level up!
- Inflection points introGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.4 (EK)
, FUN‑4.A.5 (EK)
, FUN‑4.A.6 (EK)
Learn
Practice
- Analyze concavityGet 3 of 4 questions to level up!
- Find inflection pointsGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.7 (EK)
Practice
- Second derivative testGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.10 (EK)
, FUN‑4.A.9 (EK)
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
, FUN‑4.A.10 (EK)
, FUN‑4.A.11 (EK)
Learn
Practice
- Justification using first derivativeGet 3 of 4 questions to level up!
- Justification using second derivativeGet 3 of 4 questions to level up!
- Connecting f, f', and f'' graphicallyGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.B (LO)
, FUN‑4.B.1 (EK)
, FUN‑4.C (LO)
, FUN‑4.C.1 (EK)
Learn
Practice
- OptimizationGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.D (LO)
, FUN‑4.D.1 (EK)
, FUN‑4.E (LO)
, FUN‑4.E.1 (EK)
, FUN‑4.E.2 (EK)
Practice
- Tangents to graphs of implicit relationsGet 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑4 (EU)
, FUN‑4.A (LO)
Learn
- No videos or articles available in this lesson
Practice
- Analyze functions (calculator-active)Get 3 of 4 questions to level up!
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