AP Calc Review

Derivatives

100

The slope of the function f(x)=x⁵-3x³-28

5x⁴-9x²

200

y=-4(-4x²+8x)⁶ find dy/dx

dy/dx=-24(-4x²+8x)⁵(-8x+8)

300

x^1/4cosx, find dy/dx

dy/dx=(1/4 x^-3/4)(cosx)+(-sinx)(x^1/4) or (cosx-4xsinx)/4x^3/4

400

y=(2+x³)/(1+4x), find dy/dx in simplified form

dy/dx=(8x³+3x²-8)/(1+4x)²

500

d/dx[f'(x)*g'(x)] such that x=1

f(x)=5x²-8x

g(x)=x³-4x²

54

Limits

100

The limit as x approaches 4 from the right f(x) = (10-x²) x>4  (8-2x) x<4

-6

200

The limit as x approaches 2 (x²+3x-10)/(x-2)

7

300

limit as x approaches infinity (72x⁶-18x³)/(6x⁶-12x)

12

400

limit as x approaches 0 (x³-7x)/x³

DNE

500

The limit as x approaches 7 (x²-4x-21)/(3x²-17x-28)

2/5

Asymptotes

100

find the horizontal asymptotes for f(x)=(x³-1)/(x²-1)

no horizontal asymptotes

200

find the horizontal asymptote for (5x⁵-10x+1)/(10x³-20x⁵+15)

-5/20 or -1/4

300

find the vertical asymptotes of f(x)=(x²-4x-5)/(x²-x-2)

x=2

400

find the vertical asymptotes of f(x)=(x²+x-42)/(-2x³+6x²+36x)

x=-3 and x=0

500

Find all asymptotes on the function 

f(x) = x²+7x+7 / 3x²-8x+4

                                                             

x=2/3

y=1/3

Integrals

100

Integrate f(x)=3x²-4x+1

x³-2x²+x+c

200

Integrate f(x) = 5x¹⁰-20x³+1/3x-9x⁴ from -4 to -4

0

300

Let f be a continuous function such that integral (4,6) f(x)dx=-1 and integral (2,6) f(x)dx=9. what is the value of integral (4,2) f(x)dx?

-10

400

Integrate x/(1+4x²)²

-1/(1+4x²)+c

500

Integrate f(x)=(3x³-x²+2x-4)/((x²-3x+2)^1/2) from 0 to 1

-2.981

Fun Chart

100

Inflection point =

Turning point

200

f(x) is increasing or decreasing. f'(x) is...

positive or negative

300

f(x) has a max/min when...

f'(x) crosses x-axis or DNE

400

f"(x) is positive. f(x) is....

concave up

500

f"(x) = 0 or DNE when...

f(x) has an inflection point

f'(x) has a turning point