Organize the following into 2
categories: DERIVATIVES & INTEGRALS
Slope of a Tangent Line
Given Velocity, Find Displacement
Find where a function is concave down
Riemann Sums
Find an inflection point
Chain Rule
Finding a Rate of Change
Area between Curves
Area under a curve
Product Rule
Volume of a Solid
Slope of a Curve
Find a critical point
U-Substitution
Finding a maximum of a function
Find where a function is increasing
Instantaneous Rate of Change
Given a Rate, Find a Total
Given Acceleration, Find Distance
Anti-Derivative
Calculus BC Unit 1 Day 1
Little Review
Where have we been
Where are we going
Where Have We Been
Calc AB Break Down
1) Limits
2) Derivatives
3) Applications of Derivatives
4) Integrals
5) Application of Integrals
Limits Graphically
Limits Algebraically
Methods:
1) Plug in
2) Factor
3) Getting Sneaky (Multiplying by “1”)
4) Some you just have to remember
Big Point of Limits: Continuity
Derivatives!!! Ready?!?!
Names:
Slope of a Tangent Line
Slope of the Curve
Instantaneous Rate of Change
Examples of Derivatives we’ve Learned
d 2
1) ( x + 5x + 3)
dx
d x
2) ( e cos x )
dx
d æ ln x ö
3) ç
÷
dx è tan x ø
d
4) (sin(e3x ))
dx
What the Derivatives tells us!
Applications of Derivatives
1)
2)
3)
4)
5)
Equation of Tangent Line
Equation of Normal Line (perpendicular)
Finding Max & Minimums
Related Rates Problems
PVA
We will do examples of these as warm ups over
the next couple of days!
Integrals
Integrals are Anti-Derivatives!
1) ò 4x + 3dx
2
2) ò sec xdx
2
4
3) ò xdx
2
Applications of Integrals
1)
2)
3)
4)
5)
Area between curve and x-axis
Area between 2 curves
Volumes of Solids
Integrating a Rate to find a Total
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!
Integration methods
1) U-Substitution  Reverse Chain Rule
1) Integration By Parts  Reverse Product Rule
U-Sub Practice (Hint – Find the insides)
1)
2)
3)
Integration by Parts – 2 Functions
being multiplied!
Given
Find
Steps:
1) Label f(x) and g’(x)
2) Find their counterpart
3) Plug in and Evaluate the Integral
Hardest Part: Labeling f(x)
Here is a HINT!  This is NEW!!!!
Pick f(x) by L. I. A. T. E.
Examples
Coming Up! Calculus BC
Fancy Functions
Unit 1: Polar
Unit 2: Parametric & Vector
Unit 3: More Applications of Integrals
Series
Unit 4: Infinite Series
Unit 5: Power and Taylor Series