Ap Calc Ab

Front 1

find the zeros

Back 1

set function = 0, factor or use quadratic equation if
quadratic, graph to find zeros on calculator

Front 2

find equation of the line tangent to f(x) on [a,b]

Back 2

take derivative: f'(a) = m

use y - y1 = m(x - x1)

Front 3

find equation of the line normal to f(x) on [a,b]

Back 3

same as above but take the negative reciprocal of the derivative at a (f'(a))

Front 4

show that f(x) is even

Back 4

show that f(-x) = f(x)

symmetric to y-axis

Front 5

show that f(x) is odd

Back 5

show that f(x) = -f(x)

symmetric to origin

Front 6

find the interval where f(x) is increasing

Back 6

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

Front 7

find interval where the slope of f(x) is increasing

Back 7

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

Front 8

find the minimum value of a function

Back 8

make a sign chart of f'(x), find all relative minimums
and plug those values back into f(x) and choose the
smallest

Front 9

find the minimum slope of a function

Back 9

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

Front 10

find critical values

Back 10

express f'(x) as a fraction and set both numerator and denominator equal to zero

Front 11

find inflection points

Back 11

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 +)

Front 12

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

Back 12

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)

Front 13

show that f(x) is continuous

Back 13

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

Front 14

find vertical asymptotes of f(x)

Back 14

do all factor/cancel of f(x) and set denominator = 0

Front 15

find horizontal asymptotes of f(x)

Back 15

find lim as x approaches infinity- of f(x) and lim as x approaches infinity+ of f(x)

Front 16

find the average rate of change of f(x) on [a,b]

Back 16

find (f(b) - f(a))/(b-a)

Front 17

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

Back 17

find f'(a)