#### A Summary of Curve Sketching Lesson 4.6 How It Was Done BC (Before Calculators) • How can knowledge of a function and it's derivative help.

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A Summary of Curve Sketching Lesson 4.6 How It Was Done BC (Before Calculators) • How can knowledge of a function and it's derivative help.

A Summary of Curve
Sketching
Lesson 4.6
How It Was Done BC
(Before Calculators)
• How can knowledge of a function and it's
derivative help graph the function?
Regis might be calling
for this information!
• How much can you tell about the graph of a
function without using your calculator's
graphing?
Algorithm for Curve Sketching
• Determine domain, range of the function
• Determine critical points
Places where f ‘(x) = 0
• Plot these points on f(x)
• Use second derivative f’’(x) = 0
Determine concavity, inflection points
• Use x = 0 (y intercept)
• Find f(x) = 0 (x intercepts)
• Sketch
Recall … Rational Functions
an x n ...
m
bm x ...
• Leading terms dominate
m = n => limit = an/bm
m > n => limit = 0
m < n => asymptote linear diagonal
or higher power polynomial
Finding Other Asymptotes
• Use PropFrac to get
r
y m( x) b
d ( x)
• If power of numerator is larger by two
result of PropFrac is quadratic
asymptote is a parabola
Example
• Consider
• Propfrac gives
x 2x 7x
3
2
x 5 x 3x 3
5
4
Example
• Note the
parabolic asymptote
Other Kinds of Functions
• Logistic functions
• Radical functions
• Trig functions
10
h( x )
2 3e x / 2
y x 16 x 2
1
f ( x) cos x cos 2 x
2
Assignment
• Lesson 4.6
• Page 255
• Exercises 1 – 61 EOO