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17 Cards in this Set

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find the zeros
set function = 0, factor or use quadratic equation if
quadratic, graph to find zeros on calculator
find equation of the line tangent to f(x) on [a,b]
take derivative: f'(a) = m

use y - y1 = m(x - x1)
find equation of the line normal to f(x) on [a,b]
same as above but take the negative reciprocal of the derivative at a (f'(a))
show that f(x) is even
show that f(-x) = f(x)

symmetric to y-axis
show that f(x) is odd
show that f(x) = -f(x)

symmetric to origin
find the interval where f(x) is increasing
find f'(x), set both numerator and denominator to
zero to find critical points, make sign chart of f'(x) and determine where it is positive
find interval where the slope of f(x) is increasing
find the derivative of f'(x) = f"(x), set both
numerator and denominator to zero to find critical
points, make sign chart of f"(x), and determine where
it is positive
find the minimum value of a function
make a sign chart of f'(x), find all relative minimums
and plug those values back into f(x) and choose the
smallest
find the minimum slope of a function
make a sign chart of the derivative of f'(x) = f"(x), find all relative minimums and plug those values back into f'(x) and choose the smallest
find critical values
express f'(x) as a fraction and set both numerator and denominator equal to zero
find inflection points
express f"(x) as a fraction and set both numerator and denominator equal to zero; make sign chart of f"(x) to find where f"(x) changes sign (+ to – or – to +)
show that lim as x approaches a of f(x) exists
show that the lim f(x) is the same from the left and right

lim as x approaches a- of f(x) = lim as x approaches a+ of f(x)
show that f(x) is continuous
show the following:

1) that lim as x approaches a of f(x) exists

2) that f(a) exists

3) that the lim as x approaches a of f(x) = f(a)
i.e. if you're given a function x^2+x+3, and you want to find the lim as x approaches 4 (just some a), then you plug in 4 in the function
find vertical asymptotes of f(x)
do all factor/cancel of f(x) and set denominator = 0
find horizontal asymptotes of f(x)
find lim as x approaches infinity- of f(x) and lim as x approaches infinity+ of f(x)
find the average rate of change of f(x) on [a,b]
find (f(b) - f(a))/(b-a)
find instantaneous rate of change of f(x) on a
find f'(a)