Flip Book Directions
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AP Calculus AB Flip Book Directions Tab 1: AP Calculus AB **Flip Through Every Day!** Tab 2: IVT | MVT | Explain f' ( a) (Create three columns) Column 1: Q: Does there exist at least one x=c, such that f ( c) =K for a< c< b? A: Yes, by IVT, since f is continuous and f ( a) =¿_____¿ K< ¿_____ ¿ f ( b). Column 2: Q: Must there exist at least one x=c, such that f ' ( c) =K for a< c<b? A: Yes, by MVT, since f is differentiable and continuous and f ( b ) −f ( a) b−a =K. Column 3: Q: Explain the meaning of f' ( a) in context of the problem. A: At time t=a (units), the [state the function in words] is [increasing or decreasing] at a rate of [absolute value of answer with units]. Tab 3: Implicit Differentiation (Create two columns) Column 1: Example 1 (Standard) Column 2: Example 2 (Equation of a tangent line using implicit differentiation) Tab 4: Area/Volume Top Color: Geometry Formulas! (Area of a…) Square with side s : A=s 2 Rectangle with base b, height h : A=bh Isosceles right triangle with leg l : A= 1 2 l 2 Equilateral right triangle with side s : A= √ 3 4 s 2 Semi-circles with diameter d : A= π 8 d 2
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Transcript of Flip Book Directions
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 __________.
Column 2: Q: Must there exist at least one , such that for ?A: Yes, by MVT, since is differentiable and continuous and .
Column 3: Q: Explain the meaning of in context of the problem.A: At time (units), the [state the function in words] is [increasing or decreasing] at a rate of [absolute value of answer with units].Tab 3: Implicit Differentiation (Create two columns)Column 1: Example 1 (Standard)
Column 2: Example 2 (Equation of a tangent line using implicit differentiation)Tab 4: Area/VolumeTop Color: Geometry Formulas! (Area of a)Square with side Rectangle with base , height Isosceles right triangle with leg Equilateral right triangle with side Semi-circles with diameter
Bottom Color: Examples (See Area/Volume Quiz)Tab 5: U-Sub | FTC | Student Choice (Create three columns)Column 1:Example 1Example 2
Column 2: Example 1: Example 2:
Example 3:
Column 3:You decideTab 6: Motion: position/velocity/accelerationTop Color: Examples
Bottom Color: pos/vel/accRe-Write When you see ThinkTab 7: Extrema/ConcavityTop Color: GRAPHICALLYIf is given as a graph, then is increasing when is positiveis 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:ALGEBRAICALLYExample of finding intervals of inc/decExample of finding intervals of concave up/concave downExample of finding absolute extremaTab 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
Column 2:
Column 3: If and are inverses (i.e., ) and , then
Bottom Color:Column 1: Examples of chain/product/quotient
Column 2:Examples of trig and transcendentals
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.
