4.6 curve sketching thurs dec 11 do now find intervals of increase/decrease, local max and mins,...
TRANSCRIPT
![Page 1: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/1.jpg)
4.6 Curve SketchingThurs Dec 11
Do Now
Find intervals of increase/decrease, local max and mins, intervals of concavity, and
inflection points of
![Page 2: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/2.jpg)
HWReview
![Page 3: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/3.jpg)
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
![Page 4: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/4.jpg)
• 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
![Page 5: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/5.jpg)
• 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
![Page 6: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/6.jpg)
Ex 1
• Sketch
![Page 7: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/7.jpg)
Ex 2• Draw a graph of
showing all significant features
![Page 8: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/8.jpg)
You try
• Draw a graph of
showing all significant features
![Page 9: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/9.jpg)
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
![Page 10: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/10.jpg)
4-6 Sketching More FunctionsFri Dec 12
• Do Now
• Find all important values and sketch the function
![Page 11: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/11.jpg)
HW Review p.254 #
• book
![Page 12: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/12.jpg)
Closure
• HW: p.254 #1-35, 41-69 all other odds
• 4.2-4.6 Quiz
![Page 13: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/13.jpg)
4.6 More SketchingMon Dec 15
![Page 14: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/14.jpg)
Do Now
• Graph the function
showing all significant features
![Page 15: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/15.jpg)
HW Review
![Page 16: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/16.jpg)
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)
![Page 17: 4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of](https://reader035.vdocument.in/reader035/viewer/2022072011/56649dde5503460f94ad7a41/html5/thumbnails/17.jpg)
Closure
• Journal Entry: How do the 1st and 2nd derivative help us when sketching a function?
• HW: 4.5-4.6 Quiz Tomorrow