2.1-2.2 Review

Average Rate Of Change

100

Definie what Average Rate of Change is?

Slope between 2 points 

200

What is the formula to solve for average rate of change?

m=(y₁-y₁)/(x₂-x₁)

300

Find the average rate of change on the interval 2≤x≤6 of the function f(x)=3x²-4x+1.

f(2)=5   ,     f(6)=85

85-5=80 ,    6-1=4

80/4 =20

400

A rental car company tracks how many miles a costumer has driven.

At 10:00am costumer A has driven 32,450 miles

and At 1:00 pm costumer A has driven 32,605 miles

Find the average rate of change of miles driven between 10:00am And 1:00pm.

10:00am = 0 hours     ,      1:00pm = 3 hours

32,605 miles - 32450 miles =155 miles Driven by costumer A

155/3=51.66666

500

Find the average rate of change of cos(x)*sin(x) on the interval [0,pi]

f(pi)=cos(pi)*sin(pi)=0

f(0)=cos(0)*sin(0)=0

(cos(pi)*sin(pi))-(cos(0)*sin(0)/(pi-0)=

 ((-1*0)-(1*0))/pi= 

0/pi=0

Definitions

100

What is Instantaneous Rate of Change?

The slope at one point

200

What is a tangent line?

A line that goes through one point on the curve and has the same slope as that point. 

300

What is The Normal ”Orthogonal” Line?

A line that goes through one point and has a perpendicular slope 

400

What is the formula for Alternate form?

f’(c)=Lim_x->c  (f(x)-f(c))/ (x-c)

        

500

What is the formula for the Difference Quotient or Limit Definition of the Derivative?

f’(x)= lim_h->0(f(x+h)-f(x))/h

Find the Derivative without and x-value

100

Find the derivative of f(x)=x+5

f’(x)=1

200

Find the derivative of f(x)=3x+2

f’(x)=3

300

Find the derivative of f(x)=x²+x-1

f’(x)=2x+1

400

Find the Derivative of f(x)=3x²-4x+1

f’(x)=6x-4

500

Find the derivative of f(x)=5x³-2x+7

f’(x)=15x²-2

Find the Derivative when and x-value is given

100

Find the derivative of f(x)=1/x  at x=3

f’(x)=-1/9

200

Find the derivative of f(x)=3x²   when x=2

f’(x)=6x

f’(2)=12

300

Find the derivative of f(x)=5x³    at  x=1

f’(x)=15x²

f’(1)=15

400

Find the derivative of f(x)=5x²+3x-10 at x=1

f’(x)=10x+3

f’(6)=13

500

Find the derivative of f(x)=4x³-2x+7   when   x=2

f’(x)=12x²-2

f’(2)=46

Random/Fun Facts

100

How many people are in this class?

17

200

Who gave the US the Statue of Liberty

France

300

What US state is the closest to Russia?

Alaska with 51 miles between them

400

What is Mrs. Foltz Daughters name

Peyton

500

How many countries are in the UK?

Bonus Points if you can name them.

4 countries

England, Northern Ireland, Wales, Scotland