organize the following into 2 categories: derivatives & integrals slope of a tangent line slope...
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Where Have We Been Calc AB Break Down 1)Limits 2)Derivatives 3)Applications of Derivatives 4)Integrals 5)Application of IntegralsTRANSCRIPT
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Organize the following into 2 categories: DERIVATIVES & INTEGRALS
Slope of a Tangent LineSlope of a Curve
Instantaneous Rate of Change
Find where a function is increasing
Find where a function is concave down
Find an inflection point
Find a critical point
Finding a maximum of a function
Finding a Rate of Change
Chain Rule
Product RuleGiven a Rate, Find a TotalArea under a curve
Area between Curves
Volume of a Solid
U-Substitution
Given Acceleration, Find Distance
Given Velocity, Find Displacement
Riemann Sums
Anti-Derivative
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Calculus BC Unit 1 Day 1
Little ReviewWhere have we beenWhere are we going
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Where Have We Been
Calc AB Break Down1) Limits2) Derivatives3) Applications of Derivatives4) Integrals5) Application of Integrals
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Limits Graphically
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Limits Algebraically
Methods:1) Plug in2) Factor3) Getting Sneaky (Multiplying by “1”)4) Some you just have to remember
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Big Point of Limits: Continuity
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Derivatives!!! Ready?!?!Names:Slope of a Tangent LineSlope of the CurveInstantaneous Rate of Change
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Examples of Derivatives we’ve Learned
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What the Derivatives tells us!
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Applications of Derivatives
1) Equation of Tangent Line2) Equation of Normal Line (perpendicular)3) Finding Max & Minimums4) Related Rates Problems5) PVA
We will do examples of these as warm ups over the next couple of days!
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IntegralsIntegrals are Anti-Derivatives!
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Applications of Integrals
1) Area between curve and x-axis2) Area between 2 curves3) Volumes of Solids4) Integrating a Rate to find a Total5) Average Value of a Function (Actually didn’t
cover… woops! We will though!)
We will do examples of these as warm ups over the next couple of days!
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Integration methods
1) U-Substitution Reverse Chain Rule
2) Integration By Parts Reverse Product Rule
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U-Sub Practice (Hint – Find the insides)
1)
2)
3)
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Integration by Parts – 2 Functions being multiplied!
Given Find
Steps:1) Label f(x) and g’(x)2) Find their counterpart3) Plug in and Evaluate the Integral
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Hardest Part: Labeling f(x)
Here is a HINT! This is NEW!!!!
Pick f(x) by L. I. A. T. E.
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Examples
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Coming Up! Calculus BC
Fancy FunctionsUnit 1: PolarUnit 2: Parametric & Vector
Unit 3: More Applications of Integrals
SeriesUnit 4: Infinite SeriesUnit 5: Power and Taylor Series