AP Calculus

Homework due next class-

Test Corrections

1,3,5 on page 171

Question 3 of Part II implicit class sheet

In class we went over the homework. Here are the problems we went over and the equations we went over.

The homework is to finish test corrections for tuesday, and study for a quiz on identities and the unit circle.

We went over the homework problems.  Here is a sample:

Went over Trig identities:

Our homework is on page 143 problems 1-35 odds and review Power Rule, Chain Rule, Product Rule, and Quotient Rule for the quiz on thursday.

Went over homework

Quotient Rule:

identities:

P. 134 – Product Rule # 1-21 odd as many as needed to be comfortable. No Quiz.

The Chain Rule.

A composite function uses the output of one function for the input of the other function: f(g(x)).

Trigonometric applications of the Chain Rule

Simple and Composite uses of the chain rule

Trig stuff, and note the use of the SQUEEZE THEOREM at the end

Derivatives- Displacement, Velocity, Acceleration

Anti- Derivative= integral= undoing the derivative

Parametric Mode
-Can be changed under MODE menu. Click PAR
-Can be used for particle problems to analyze a one or two dimensional motion
-Easier to see if you use the bouncing ball when you graph it
-You can plot displacement, velocity (derivative of displacement), and acceleration (2nd derivative of displacement and derivative of velocity) in this mode just like in function mode
-It’s useful because you can see the motion, unlike in function mode

Derivative of Acceleration= a jerk

Questions of Worksheet
16

30

38

Chain Rule

Homework- ON ASSIGNMENT CALENDAR

CLASS OCTOBER 14 2009

WE GOT OUR TESTS BACK
THEY WERE SCALED

QUESTIONS THAT WE WENT OVER:
PART 1: 2,4,6,7
QUESTION 2: REMEMBER TO FACTOR OUT AS MUCH AS POSSIBLE-SYNTHETIC DIVISION ON CUBIC. ANSWER B

QUESTION 4, WHAT DOES THIS FUNCTION LOOK LIKE?
ANSWER: C
THE LIMIT OF THE FUNCTION APPROACHING INFINITY IS ZERO, SO THE X AXIS IS THE VERTICAL ASYMPTOTE.
THE DENOMINATOR IS THE DIFFERENCE OF SQUARES OF ONE, MEANING THERE ARE TWO VERTICAL ASYMPTOTES, AT 1 AND -1.

QUESTION  6: WHAT MUST BE TRUE ABOUT THE FUNCTION?
ANSWER: E
ALL OF THESE OPTIONS CAN BE TRUE, BUT NONE OF THEM HAVE TO BE.

QUESTION 7: SOLVE FOR K
ANSWER: -1/2
MAKE SURE TO WRITE
OR ELSE IT MAKES NO SENSE

PART 2

QUESTION 3: FIND f ‘(2)
ANSWER: f ‘(2)=42
THERE WERE MULTIPLE WAYS TO DO THIS, ALL USING SOME FORM OF THE DIFFERENCE QUOTIENT.

QUESTION 5: FIND DISCONTINOUS POINTS AND LABEL
THIS CAME DOWN TO FACTORING CORRECTLY AND KNOWING YOUR DIFFERENT TYPES OF DISCONTINUITY

THEN WE PLAYED A GAME PLOTTING DERIVATIVE FUNCTIONS
FRONT TEAM WON!!!!!

DISPLACEMENT, VELOCITY, AND ACCELERATION
s(t)= DISPLACEMENT
v(t)=VELOCITY
a(t)=ACCLERATION

THIS LED TO THE DISCOVERY OF SECOND DERIVATIVES:

s’(t)=v(t)
s”(t)=v’(t)=a(t)

AKA: THE DERIVATIVE EQUATION OF A DISPLACEMENT EQUATION IS VELOCITY, AND THE DERIVATIVE EQUATION OF A VELOCITY EQUATION IS ACCELERATION, MAKING THE SECOND DERIVATIVE OF DISPLACEMENT ACCELERATION.

Binomial Expansion

Example:

Definition of Derivative: f ‘ (x)

Forward Difference (quotient difference)=

Backward Difference=

Symmetric Difference (often used with table)=

At a Point=

Derivative Worksheet:

1.

2.

f’(x)=(-2)

POWER FUNCTION RULE (also on page 92)

Power function continued…

Example 1

Example 2

Calculator:

On the AP exam, a calculator can be used for finding x intercepts, numerical derivatives and numerical integration.

To find the derivative at x=2 when f(x)=x^5:

Plug in x^5 as Y1 –> Math –> Option #8 –>and then plug in nDeriv(Y1,x,2)–> 2nd calc gets a value.

This will get you an answer of 80.00004.  Don’t forget that .00004 is a small margin of error.

PROPERTIES OF DIFFERENTIATION (pg 93)

NOTATION OF DERIVATIVE

Derivative with respect to x of function y:

REMINDER:

HW: pg 95- 10 Qs, #1-25 odd

-Challenge problem

-Major Quiz Friday

finds the slope of the tangent line at f=c

more specific; at a point

use when you have a function and a point

any function at any point

can be used for every problem

as x and x+h get closer, it approaches the slope of the tangent line.

Derivative: Slope of the tangent line.

Find when taking limit of the slope of the secant line

Derivative Worksheet:

2. The answer is -3 because it is the slope of the secant line. Since the equation 9-3x is linear, it has the same slope.

4.

7.

10.

review of limits terminology:

HOMEWORK: limits graded worksheet

Challenge problem due 10/14

work on derivative packet

Major quiz Friday 10/9