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17 Cards in this Set
 Front
 Back
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 yaxis 

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))/(ba)


find instantaneous rate of change of f(x) on a

find f'(a)
