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AP Calculus

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Section 1

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Point of inflection

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Calculus Math

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Mar 1, 2020

Cards (30)

Section 1

(30 cards)

Point of inflection

Front

the point where the graph changes concavity

Back

Sigma E i^3

Front

((N^2)(n+1)^2)/4

Back

Mean Value Theorem

Front

if f(x) is continuous and differentiable, then there exists a number, c, in (a,b) such that f '(c) = [f(b) - f(a)]/(b - a)

Back

Average velocity

Front

F(b)-f(a)/b-a

Back

Cscx

Front

-cscxcotx

Back

Product rule

Front

ab = a'b + ab'

Back

Sigma E c =

Front

Cn

Back

Sigma E i =

Front

(N(n+1))/2

Back

Cosx

Front

-sinx

Back

Sinx

Front

cosx

Back

Tanx

Front

sec^2x

Back

Limits at Infinity

Front

describes the end behavior of a function 1. If degree of numerator > the degree of denominator, DNE 2. If degree of numerator < the degree of denominator, f(x) = 0 3. If degree of numerator = the degree of denominator, f(x) = ratio

Back

Secx

Front

secxtanx

Back

removable discontinuity

Front

a "hole" in a graph - can be removed once factored out

Back

Rolle's Theorem

Front

if f(x) is continuous on [a,b] and differentiable on (a,b), and if f(a)=f(b), then there is at least one point (x=c) on (a,b) [DON'T INCLUDE END POINTS] where f'(c)=0

Back

Chain rule

Front

F'(x) = f'(u)(u')

Back

Limit Definition

Front

lim h->0 f(x+h)-f(x)/h

Back

Definition of Continuity at a Point

Front

A function f is continuos at x=c when these 3 conditions are met: 1. f(c) exists 2. lim f(x) exists x->c 3. lim f(x) = f(c) x->c

Back

Cotx

Front

-csc^2x

Back

Intermediate value theorem

Front

If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k

Back

Differing behavior

Front

Approaches a different # from the right than it approaches from the left

Back

Test for concavity

Front

Let f be a function whose second derivative exists on an open interval I. 1. If f''(x) > 0 for all x in I, then the graph of f is concave upward in I. 2. If f''(x) < 0 for all x in I, then the graph of f is concave downward in I.

Back

First Derivative Test

Front

Used to determine where a function's graph has a min/max and is increasing or decreasing - if f'(x) changes from pos. To neg. at a critical #, then f has local max - if f'(x) changes from neg. to pos. At a critical # then f has a local min

Back

nonremovable discontinuity

Front

A vertical asymptote - the value(s) cannot be cancelled with an expression on top of the fraction

Back

Second Derivative Test

Front

1. Find critical numbers 2. Plug critical numbers into the 2nd derivative 3. If result is positive —> minimum If result is negative —> maximum If result is 0 —> use 1st Derivative test

Back

Absolute Extrema

Front

1. Find critical #s on interval 2. Evaluate function at each endpoint & critical number 3. Smallest value = minima & largest value = maxima

Back

Oscillating behavior

Front

F(x) oscillates between 2 fixed values

Back

Sigma E i^2

Front

(N(n+1)(2n+1))/6

Back

Unbounded behavior

Front

F(x) increases or decreases without bound (vertical asymptote)

Back

Quotient Rule

Front

a/b = a'b-ab'/b^2

Back