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4.0(1)

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Hint

1

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

-Critical Point or undefined and endpoints

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2

Local Minimum

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

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3

Local Maximum

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

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4

Point of Inflection

Concavity Changes

(+,0,-) or (-,0,+)

(+,und,-) or (-,und,+)

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5

D/dx(sinx)

Cosx

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6

D/dx(cosx)

-sinx

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7

D/dx(tanx)

Sec²x

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8

D/dx(cotx)

-csc²x

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9

D/dx(secx)

Secxtanx

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10

D/dx(cscx)

-cscxcotx

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11

D/dx (lnx)

1/x × derivative of x

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12

D/dx(eⁿ)

Eⁿ derivative of n

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13

∫Cosx

-Sinx

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14

∫-sinx

Cosx

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15

∫Sec²x

Tanx

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16

∫-csc²x

Cotx

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17

∫Secxtanx

Secx

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18

∫-cscxcotx

Cscx

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19

∫1/n

Ln(n)

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20

∫Eⁿ

Eⁿ

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21

When doing integrals never forget

Constant (+c)

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22

∫Axⁿ

A/n+1(xⁿ⁺¹)+C

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23

∫Tanx

Ln|secx|+c

-Ln|cosx|+c

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24

∫Secx

Ln|secx+tanx|+c

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25

D/dx(sin⁻¹x)

1/√1-x²

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26

D/dx(cos⁻¹x)

-1/√1-x²

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27

D/dx(tan⁻¹x)

1/1+x²

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28

D/dx(cot⁻¹x)

-1/1+x²

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29

With derivative inverses

You plug in the number of the trigonometric function into x

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30

D/dx(sec⁻¹x)

1/|x|√x²-1

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31

D/dx(csc⁻¹x)

-1/|x|√x²-1

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32

D/dx(aⁿ)

aⁿln(a)

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33

D/dx(Logₙx)

1/xln(a)

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34

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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35

Product Rule

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

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36

Quotient Rule

LoDHi-HiDLo/LoLo

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37

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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38

*f* relative max→*f* ‘ goes from

Positive to negative

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39

*f* relative min→*f* ‘ goes from

Negative to positive

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