4.6 Curve SketchingThurs Dec 11

Do Now

Find intervals of increase/decrease, local max and mins, intervals of concavity, and

inflection points of

HWReview

Curve Sketching

• Before we can start curve sketching, it is beneficial to find several values:

• Domain– Always find the domain of f(x) first, so you know

where we need to be sketching and where we don’t

• Vertical Asymptotes– For any point not in the domain of f(x), check the

limit approaching that point to see if there is a vertical asymptote

• First Derivative Info– Determine where f(x) is increasing and

decreasing– Find any local extrema (x,y coordinates)

• Vertical Tangent Lines– At any undefined point in f’(x) and in the

domain of f(x), check the limit approaching that value to see if there is a vertical tangent

• Second Derivative Info– Determine where the graph is concave up

and concave down– Locate any inflection points (x,y)

coordinates

• Horizontal Asymptotes– Check the limit of f(x) as x approaches +/-

infinity

Ex 1

• Sketch

Ex 2• Draw a graph of

showing all significant features

You try

• Draw a graph of

showing all significant features

Closure

• Find all the important values of the following function, and then graph it

• HW: p.254 #1-35 41-69 EOO no 21

• 4.2-4.6 Quiz Wed or Thurs

4-6 Sketching More FunctionsFri Dec 12

• Do Now

• Find all important values and sketch the function

HW Review p.254 #

• book

Closure

• HW: p.254 #1-35, 41-69 all other odds

• 4.2-4.6 Quiz

4.6 More SketchingMon Dec 15

Do Now

• Graph the function

showing all significant features

HW Review

4.5-4.6 Quiz Review

• 4.5 L’Hopital’s Rule

• 4.6 Curve Sketching– This section requires 1st and 2nd derivative

info (4.2-4.4)

Closure

• Journal Entry: How do the 1st and 2nd derivative help us when sketching a function?

• HW: 4.5-4.6 Quiz Tomorrow