AP Calculus AB Flip Book Directions

Tab 1: AP Calculus AB **Flip Through Every Day!**

Tab 2: IVT | MVT | Explain () (Create three columns)

Column 1: Q: Does there exist at least one = , such that () = for < < ?

A: Yes, by IVT, since is continuous and () =_____<

Tab 7: Extrema/Concavity

Top Color: GRAPHICALLY

If is given as a graph, then

is increasing when is positive

is decreasing when is negative

has a relative max when changes from positive to negative

has a relative min when changes from negative to positive

has a point of inflection when changes from increasing to decreasing OR vice versa

// +/

Example (Draw a piecewise linear graph; call it ; answer the questions above)

Bottom Color: ALGEBRAICALLY

Example of finding intervals of inc/dec

Example of finding intervals of concave up/concave down

Example of finding absolute extrema

Tab 8: Chain Rule/Product Rule/Quotient Rule | Trig/ ()/ | Derivative of inverse (Create three columns)

Top Color:

Column 1: Chain: If () = (()) = ()(), then () = (())()

Product: If () = ()() = ()(), then () = ()() + ()()

Quotient: If () =()

()= (

) (), then () =

()()()()

(())2

Column 2:

Column 3: If and are inverses (i.e., () = 1()) and () = , () = , then

() =1

(())=

1

()=

1

Bottom Color:

Column 1: Examples of chain/product/quotient

Column 2: Examples of trig and transcendentals (ln , )

Column 3: Examples of derivative of inverse function

Highlighted portions: Find your own examples; Dixie Rosss Big Picture packet is a good place to look.

() () sin cos tan sec2 sec sec tan cos sin cot csc2 csc csc cot ln 1