AP Calculus AB Flashcards

The Power Rule:

The Product Rule

The Quotient Rule

The Chain Rule

(d/dx) sin x

cos x

(d/dx) cos x

-sin x

(d/dx) tan x

(d/dx) sec x

sec x tan x

(d/dx) cot x

(d/dx) csc x

(d/dx) e^f(x)

(d/dx) a^f(x)

(d/dx) ln(f(x))

(d/dx) loga f(x)

(log base a of f(x))

(d/dx) arcsin x

(d/dx) arctan x

Definiton of Derivative

Definition of the Derivative of a Function

Speed

Displacement

Total distance traveled

When is speed increasing?

When is speed decreasing (in terms of velocity and acceleration)?

When v(t) and a(t) have opposite signs

Average Rate of Change of f(x) on [a,b]

instantaneous rate of change

Mean Value Theorem (MVT)

Mean Value Theorem Picture

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.

Average Value of a Function

Intermediate Value Theorem (IVT)

Extreme Value Theorem (EVT)

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

Definition of Continuity

Squeeze Theorem

Volume - Disc Method

Volume - Washer Method

Volume of cross section perpendicular to x axis

Fundamental Theorem of Calculus - Part 1

L'Hopital's Rule

limits at horizontal asymptotes

limits at horizontal asymptotes - specific problems

limit exists when

We don't care what is happening at a, as long as the y coordinate on the left and the y coordinate on the right agree, the limit exists, and it equals the y coordinate.

Fundamental Theorem of Calculus - Part 2

Area of a trapezoid formula

Derivative of an Inverse Function

Critical Number

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.)

First Derivative Test for local extrema

Point of inflection at x=k

Second Derivative Test

Exponential growth (Use N=)

Squaring function

Domain: (-∞,∞)

Range: [0,∞)

Cubing function

Domain: (-∞,∞)

Range: (-∞,∞)

Reciprocal Function

Domain: (-∞,∞) x can't be 0.

Range: (-∞,∞) y can't be 0.

Square root function

Domain: [0,∞)

Range: [0,∞)

Exponential function

Domain: (-∞,∞)

Range: (0,∞)

Natural logarithmic function

Domain: (0,∞)

Range: (-∞,∞)

Sine function

Domain: (-∞,∞)

Range: [-1, 1]

Cosine function

Domain: (-∞,∞)

Range: [-1, 1]

Absolute value function

Domain: (-∞,∞)

Range: [0,∞)

greatest integer function

Domain: (-∞,∞)

Range: (-∞,∞)

sin(x) + C

-cos(x) + C

tan(x) + C

sec(x) + C

-cot(x) + C

-csc(x) + C

ln|x| + C

Additional definition of derivitive

f(x)-f(a)/x-a