CALC - Memorize for the AP Calculus Test

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39 Terms

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Y=f(x) must be continuous at each:

-Critical Point or undefined and endpoints

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Local Minimum

Goes (-,0,+) or (-, und, +)

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Local Maximum

Goes (+,0,-) or (+, und, -)

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Point of Inflection

  • Concavity Changes

  • (+,0,-) or (-,0,+)

  • (+,und,-) or (-,und,+)

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D/dx(sinx)

Cosx

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D/dx(cosx)

-sinx

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D/dx(tanx)

Sec²x

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D/dx(cotx)

-csc²x

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D/dx(secx)

Secxtanx

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D/dx(cscx)

-cscxcotx

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D/dx (lnx)

1/x × derivative of x

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D/dx(eⁿ)

Eⁿ derivative of n

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∫Cosx

-Sinx

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∫-sinx

Cosx

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∫Sec²x

Tanx

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∫-csc²x

Cotx

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∫Secxtanx

Secx

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∫-cscxcotx

Cscx

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∫1/n

Ln(n)

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∫Eⁿ

Eⁿ

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When doing integrals never forget

Constant (+c)

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∫Axⁿ

A/n+1(xⁿ⁺¹)+C

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∫Tanx

  • Ln|secx|+c
  • -Ln|cosx|+c
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∫Secx

Ln|secx+tanx|+c

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D/dx(sin⁻¹x)

1/√1-x²

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D/dx(cos⁻¹x)

-1/√1-x²

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D/dx(tan⁻¹x)

1/1+x²

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D/dx(cot⁻¹x)

-1/1+x²

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With derivative inverses

You plug in the number of the trigonometric function into x

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D/dx(sec⁻¹x)

1/|x|√x²-1

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D/dx(csc⁻¹x)

-1/|x|√x²-1

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D/dx(aⁿ)

aⁿln(a)

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D/dx(Logₙx)

1/xln(a)

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Chain Rule

  • Take derivative of outside of parenthesis
  • Take derivative of inside parenthesis and keep the original of what was in the parenthesis
  • For example, sin(x²+1)→ 2xcos(x²+1)
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Product Rule

d/dx first times second + first times d/dx second

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Quotient Rule

LoDHi-HiDLo/LoLo

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Fundamental Theorem of Calculus

  • ∫(a to b) f(x) dx = F(b) - F(a)
  • Basically saying that F’(x)=f(x)
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f relative max→f ‘ goes from

Positive to negative

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f relative min→f ‘ goes from

Negative to positive