Level 571 Level 573
Level 572

Curve Sketching & Analysis


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critical point
a point in the domain of the function at which the derivative is zero or undefined.
local minimum
y' goes (-, 0, +) or (-, undefined, +)
local maximum
y' goes (+, 0, -) or (+, undefined, -)
f(x) is Increasing
y' > 0
f(x) is decreasing
y' < 0
Absolute max.min
check critical values and end points
concave up
When f '(x) is increasing, f(x) is
concave down
When f '(x) is decreasing, f(x) is
point of inflection
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a
Horizontal Tangent
y' = 0 or y' = 0/1
vertical tangent
y' = DNE of y' = 1/0
slant line asymptote
If the degree of the numerator's leading term is greater than the degree of the denominator's leading term, then the horizontal asymptote is a:
zero
If the degree of the numerator's leading term is less than the degree of the denominator's leading term, then the horizontal asymptote is at:
ratio of leading coefficients
If the degree of the numerator's leading term is equal to the degree of the denominator's leading term, then the horizontal asymptote is the:
zero
If n<d, horizontal asymptote is
slant line
If n>d, horizontal asymptote is
sine
Opposite/hypotenuse
Cosine
Adjacent/hypotenuse
Tangent
Opposite/adjacent
cosecant
hypotenuse/opposite
secant
1 over cosine
cotangent
adjacent/opposite
Circle
r=acosθ or r=asinθ
x and y intercepts
first step of creating graphs
denominator = 0
there is a vertical asymptote when the ________= _______
horizontal and vertical asymptotes
step 2 of sketching graphs is
first and second derivative
third step of sketching graphs
sign analysis of f1
step 5 of sketching graphs
relative maxes or mins
step 4 of sketching graphs
inflection points
step 6 of sketching graphs
sign analysis of f2
step 7 of sketching graphs
cup
(c) a customary unit of measure equal to 8 fluid ounces
frown
concave down looks like a ________