Summary of Curve Sketching

1
Lesson 4-6

• Summary of Curve Sketching
• With Calculators

2
Quiz

• Homework Problem MVT Rolles 4-2
• Verify Rolles Theorem applies and find all cs
• f(x) -x³- 3x² 2x 5 on 0,2
• Reading questions
• What is an oblique asymptote called?
• What is f(x) called if f(-x) -f(x) for all x?

3
Objectives

• Sketch or graph a given function using your
  calculator to help you

4
Vocabulary

• None new

5
Graphing Checklist
Domain for which values is f(x) defined? x
-intercepts where is f(x) 0? y -intercepts
what is f(0)? Symmetry y-axis is f(-x)
f(x)? Origin is f(-x) -f(x)? Period is
there a number p such that f(x p)
f(x)? Asymptotes Horizontal does or
exist? Vertical for what is ? for what is ?
Division by 0 or negatives under even roots
Type in solve(f(x)0,x)
Type in f(x) x 0
Even functions
Odd functions
Trig functions
Limit as x?8
F3, limits Type in Lim(f(x),x,a)
Division by 0 (and not removed by canceling)
6
Graphing Checklist (cont)
Derivative Information Critical numbers where
does f(x) 0 or DNE? Increasing on what
intervals is f(x) 0? Decreasing on what
intervals is f(x) 0? Local extrema what are
the local max/min? Use f or f
test. Concavity Up where is f(x) gt 0? Down
where is f(x) lt 0? Inflection points where
does f change concavity?
F3 dif(f(x),x)
Copy derivative and paste into solve(f(x)0,x)
Type in f(x) x value
2nd DT Type in f(x) x critical
F3 dif(f(x),x)
Copy derivative and paste into solve(f(x)0,x)
Type in f(x) x value
Use calculator to check your info by graphing the
function. Be Careful the small screen can
lead to some tricky views
7
Example 1
f(x) -2x/(x² - 4)²
1 Graph --------------
x² 4
f(x) 2(3x² 4)/(x² - 4)³
Domain x intercepts y intercepts
Symmetry Y-axis Origin
Periodic Asymptotes H
V Critical numbers Increasing Decreas
ing Max/Min Concavity
x ? 2
None, y ? 0
y -1/4
Yes
No
No
x -2, 2
y 0
x 0
x lt 0
x gt 0
At x 0, y -1/4 is a relative max
Up xgt2 Down x lt 2
8
Example 1 Graph
9
Summary Homework

• Summary
• Calculator is a great tool that can help you with
  many things
• Derivatives
• Solutions to Equations
• Function zeros
• Functions evaluated at specific values
• Because of its small screen it can trick us to
  seeing something that isnt really there
• Homework
• pg 330-331 1, 4, 12, 15, 16