a function has this at C if f(c)>f(x) for all x in the domain of of f

Back

local max or min

Front

always there on an open interval except on a line

Back

L(x)=f(a)+f'(a)(x-a)

Front

equation for linear approximation

Back

-sinx

Front

derivative of cosx

Back

integrals

Front

if f is a function defined where f(x)>0 for a<x<b, divide the interval [a,b] into subinterval of equal width let x-initial=a, xsub1, xsub2.....=b are the end points of the subinterval. the definite one of f from a to b. represents area under the curve

Back

average velocity

Front

displacement over change in time

Back

l'hostpital's rule

Front

suppose f and g are differentiable and g'(x) doesn't equal 0 on an open interval I that contains a (except possibly at A) then limf/g as x approaches a=limf'/g' as x approaches a

Back

RlnM

Front

what lnM^R is equivalent to

Back

number of divisions under the curve

Front

n= this

Back

mean value theorum

Front

let f be a function that satisfies the following hypothesis: fi is continuous on the closed interval [a,b]. f is differentiable on the open interval (a,b). then there is a number, C, on (a,b) so that f'(c)=f(b)-f(a)/b-a

Back

intermediate value theorum

Front

suppose that f is continuous on the closed interval [a,b] and let N be any number between f(a) and f(b) where f(a) doesn't equal f(b). then there exists a number, C, in [a,b] such that f(c)=N

Back

concavity

Front

what the second derivative test checks for

Back

sec^2(x)

Front

derivative of tanx

Back

infinite discontinuity

Front

Back

continuous function

Front

f(x) is defined at a. limf(x) exists. limf(x)=f(a)

Back

cosx

Front

derivative of sinx

Back

squeeze theorum

Front

if f(x)<g(x)<h(x) when x is near A (but not A) and limf(x)=limh(x)=L then limg(x)=L

Back

(f(x+h)-f(x))/h

Front

instantaneous rate of change

Back

1/x

Front

derivative of lnx

Back

local max and mins

Front

what the first derivative test checks for

Back

removable discontinuity

Front

Back

Rolle's theorum

Front

let f be a function that satisfies the following hypothesis: f is continuous on the closed interval [a,b]. f is differentiable on the open interval (a,b). f(a)=f(b)
then there is a number c in (a,b) such that f'(c)=0

Back

net change theorum

Front

interal of F'(x)dx=F(b)-F(a)

Back

1/(1-x^2)^(1/2)

Front

derivative of sin^-1(x)

Back

-cscxcotx

Front

derivative of cscx

Back

fundamental theorum of calculus Pt. 1

Front

if g(x)=the integral from a-x of f(t)dt then g'(x)=f(x)

Back

extreme value theorum

Front

if f is contunous on a closed interval [a,b] then f attains an absolute max value f(c) and an absolute min value f(d) at some c and d in the interval [a,b]

Back

1/xlna

Front

derivative of dlogx

Back

-cscx

Front

derivative of cotx

Back

-1/(1-x^2)^(1/2)

Front

derivative of cos^-1(x)

Back

f'(x)/g'(x)

Front

derivative of lnf(x)

Back

newton's method

Front

if x-initial is an initial approximation to f(x)=0 then x sub (n+1) = f(xsubn)/f'(xsubn)

Back

jump discontinuity

Front

Back

secxtanx

Front

derivative of secx

Back

lnM-lnN

Front

what lnM/N is equivalent to

Back

limit of a function

Front

suppose f(x) is defined when x is near A (in an open interval that contains A but not neccessarily at A)

Back

chain rule

Front

f'=f'(g(x))g'(x)

Back

lnM+lnN

Front

what lnM*N is equivalent to

Back

vertical asymptote

Front

limx-->af(x)=+-infinity then A is this

Back

1/|x|(x^2-1)^(1/2)

Front

derivative of sec^-1(x)

Back

marginal cost

Front

cost to produce the next item

Back

antiderivative theorum

Front

if F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is F(x)+C (where C is an arbitrary constant)

Back

antiderivative definition

Front

F(x) is an antiderivative of f(x) on an interval I if F'(x)=f(x) for all x's in I

Back

1.) find derivative and set it equal to zero to find the critical numbers ON THE INTERVAL
2.) find values of the end points and critical points
3.) find the biggest and smallest ones ON THE INTERVAL

Front

steps to find absolute max and mins

Back

minimum value

Front

a function has this at c if f(c)<f(x) for all x in the domain of f

Back

horizontal asymptote

Front

if the limf(x)=L as x goes to positive or negative infinity then y=L

Back

fermat's theorum

Front

if f has a local max or min at c and if f'(c) exists then f'(c)=0. a critical number of a function is a numbeer c in the domain of f such that f'(x)=0 or f'(x) doesn't equal 0

Back

1/1+x^2

Front

derivative of tan^-1(x)

Back

Section 2

(10 cards)

substitution

Front

if u=g(x) is a differentiable function whose range is an interval and f is continuous on I then the integral f(g(x))g'(x)dx=integral f(u)dx

Back

displacement

Front

integral from a-b v(t)dt=s(t)|from a-b

Back

distance

Front

integral from a-b |v(t)|dt

Back

v=deltax*r^2

Front

volume of cylinder

Back

area between curves

Front

integral from a-b [f(x)-g(x)] -- upper minus lower

Back

volume

Front

let S be a solid that lies between x=a and x=b if the cross sectional area of S in the plane P subx through x and perpendicular to the x-axis is a(x) where A is a continuous function then the _____ of S is S=integral from a-b A(x)dx

Back

disk method

Front

rotated about x axis from [a,b]. pi*integral from a-b [f(x)]^2dx

Back

shells method

Front

V=2pi*integral a-b of (rh)dr. rotate along y axis and integrate along x axis (in terms of x) heigh runs parallel to axis of rotations

Back

v=(4/3)pir^3

Front

volume of sphere

Back

washer method

Front

A=pi(r outisde^2-r inside^2). V=pi*integral from a-b of (r outisde^2-r inside^2)dx