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AP Calculus Flash Cards_AB_Mrs. KU

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f'(x)-g'(x)

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Calculus Math

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Mar 14, 2020

Cards (38)

Section 1

(38 cards)

f'(x)-g'(x)

Front

Back

Extreme Value Theorem

Front

If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.

Back

Antiderivative of xⁿ

Front

Back

Constants in integrals

Front

Back

Mean Value Theorem for integrals or the average value of a functions

Front

Back

cos(x)

Front

Back

f is continuous at x=c if...

Front

Back

-cos(x)+C

Front

Back

-cot(x)+C

Front

Back

Fundamental Theorem of Calculus #1

Front

The definite integral of a rate of change is the total change in the original function.

Back

x+c

Front

Back

nx^(n-1)

Front

Back

sec²(x)

Front

Back

Horizontal Asymptote

Front

Back

Opposite Antiderivatives

Front

Back

-csc²(x)

Front

Back

sec(x)+C

Front

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

Alternative Definition of a Derivative

Front

f '(x) is the limit of the following difference quotient as x approaches c

Back

Antiderivative of f(x) from [a,b]

Front

Back

tan(x)+C

Front

Back

2nd Derivative Test for local extrema

Front

If f'(c) = 0 and f"(c)<0, there is a local max on f at x=c. If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c.

Back

First Derivative Test for local extrema

Front

Back

Adding or subtracting antiderivatives

Front

Back

Global Definition of a Derivative

Front

Back

Front

Back

-csc(x)+C

Front

Back

Fundamental Theorem of Calculus #2

Front

Back

Mean Value Theorem

Front

The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.

Back

1

Front

Back

f'(x)+g'(x)

Front

Back

cf'(x)

Front

Back

sin(x)+C

Front

Back

sec(x)tan(x)

Front

Back

Critical Number

Front

If f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined)

Back

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

Front

Back

Point of inflection at x=k

Front

Back

-sin(x)

Front

Back