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Level 573

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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 ________