1. Summary of Curve Sketching With Calculators
Lesson 4-6
Summary of Curve Sketching
With Calculators

2. Quiz Homework Problem: MVT & Rolle’s 4-2 Reading questions:
Verify Rolle’s Theorem applies and find all c’s
f(x) = -x³- 3x² + 2x 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→±∞
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) > 0?
Down – where is f’’(x) < 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 1 Graph -------------- x² – 4 Domain: x –intercepts:
f’(x) = -2x/(x² - 4)²
f’’(x) = 2(3x² +4)/(x² - 4)³
Domain:
x –intercepts:
y –intercepts:
Symmetry: Y-axis: Origin: Periodic:
Asymptotes H: V:
Critical numbers:
Increasing:
Decreasing:
Max/Min:
Concavity
x ≠ ± 2
None, y ≠ 0
y = -1/4
Yes No No
y = 0
x = -2, 2
x = 0
x < 0
x > 0
At x = 0, y = -1/4 is a relative max
Up: |x|>2 Down: |x| < 2

8. Example 1 Graph y x

9. Summary & Homework Summary: Homework:
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 isn’t really there
Homework:
pg : 1, 4, 12, 15, 16