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AP Calculus

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Section 1

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critical point

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Calculus Math

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Mar 1, 2020

Cards (29)

Section 1

(29 cards)

critical point

Front

a place where the first derivative is either zero or does not exist

Back

velocity

Front

rate of change in position with respect to its starting place

Back

extreme value theorem

Front

if f is continuous over a closed interval [a,b] then f has both a global minimum and global maximum in the interval

Back

intermediate value theorem

Front

let f be a function continuous on the closed interval [a,b]. Then for every value m between f(a) and f(b) there exists a value c, a < c < b, such that f(c)=m

Back

optimization

Front

to maximize or minimize some aspect of a system being modeled in an application

Back

Front

Back

antiderivative

Front

a function F whose derivative is f. That is F'(x)=f(x)

Back

integrand

Front

the function used in a definite integral

Back

acceleration

Front

the rate of change of the velocity of the object

Back

extrema

Front

a maximum or minimum value of a function or set

Back

continuity

Front

a place where the function and its limit must exist, and be equal to one another

Back

trapezoidal rule

Front

an approximation for area under a curve using subintervals in the shape of trapezoids

Back

monotonic

Front

a function which is increasing of decreasing over its entire domain

Back

speed

Front

the rate of motion when the direction of the motion is not an issue

Back

point of inflection

Front

a coordinate point where the concavity changes

Back

lower bound

Front

the left-most side of an interval being integrated

Back

definite integral

Front

a means for approximating area under a curve using rectangles and a limit as the number of rectangles approaches infinity

Back

rectangular approximation method (RAM)

Front

methods which vary using lefthand, righthand, or midpoint locations of the subintervals along a curve being integrated

Back

approach statement

Front

a statement that describes the behavior of a function at various locations

Back

jump discontinuity

Front

place where one-sided limits exists but have different values for one another

Back

summation notation

Front

a method for expressing a large sum in a more compact form using the Greek letter, "sigma"

Back

intial position

Front

the object's location at time t0

Back

final position

Front

the object's location at time tn

Back

upper bound

Front

the right-most side of an interval being integrated

Back

tangent

Front

a line through a point on a curve with slope equal to the curve at that point

Back

displacement

Front

the distance between the final position and initial position

Back

Front

Back

indefinite integral

Front

integrals which have no bounds and are written to represent all of the antiderivatives for a function at a given x-value

Back

derivative

Front

the slope of a line tangent to at any point x

Back