Calculus Section 3.6 Notes
Learning Targets…
1. Sketch graphs using information from a function & its
derivatives
LT: Sketch graphs using information from a function & its
derivatives
• Intercepts:
o Find and plot y-intercept: x=0
o Find and plot x-intercept(s): y=0
• Asymptotes:
o Identify vertical asymptotes: bottom=0 (non-
removable)
o Identify horizontal asymptotes: 𝒚=𝐥𝐢𝐦𝒙→±∞𝒇(𝒙)
o Use long division to find oblique (slant) asymptotes
When degree on top is 1 bigger than bottom
Ignore fraction terms (fraction → 0 in limit
process)
• Set up a table with x, f’, f”, and f
o Identify and plot relative extrema
o Identify and plot POI
o Identify increasing/decreasing intervals
o Identify concavity intervals
• Use calculator to solve for values if necessary
Graph the following showing all graphical analysis.
1)
𝑦=−1
3(𝑥3−3𝑥+ 2)
2)
𝑦=𝑥2−2𝑥+ 4
𝑥 − 2