AP Calculus AB Vocab – Flashcards
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absolute minimum
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The lowest point of a function.
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absolute maximim
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The highest point of a function.
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absolute value
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The distance between a number and the origin.
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acceleration
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The rate of change of velocity over time.
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amplitude
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The distance a function is from the axis.
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approximation
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An approximate calculation of quantity or degree or worth.
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asymptotes
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A line or curve that the graph follows closely but never touches.
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average rate of change
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(〖f(x)〗_2-〖f(x)〗_1)/(x_2- x_1 )
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average value
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(1/b-a) ∫f(x)dx from a to b
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axis of rotation
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A line about which a figure is rotated to create a solid.
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axis of symmetry
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A line of symmetry for a graph.
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base
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exponential: a in the expression a^x logarithmic: b in the expression logb x
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bounded
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When there is a range on a function or set of numbers.
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chain rule
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f'(g(x))g'(x)
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closed interval
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An interval that contains its endpoints.
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composition
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Combining two functions by substituting one function's formula in place of each x in the other function's formula.
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concave down
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A part of the graph that looks like a frown.
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concave up
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A part of the graph that looks like a smile.
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constant function
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y= constant
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continuity
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When the graph of a function is continuous.
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critical point
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A point on the graph of a function at which the derivative is either 0 or undefined.
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critical value
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The x-value of a critical point.
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decreasing function
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A function with a graph that moves downward from left to right.
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derivative
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The slope of the line tangent to a function.
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differentiability
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When a function has a well-defined derivative for each element of the domain.
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differentiation
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Obtaining the derivative of a function.
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discontinuity
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A point at which the graph is not continuous.
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distance
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The interval between two points.
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domain
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The set of x-values for which a function is defined.
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endpoints
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Points on the end of a function.
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even function
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Symmetric with respect to the y-axis.
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first derivative test
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Determines whether a point is a minimum, maximum, or neither.
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implicit differentiation
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y' = dy/dx
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increasing function
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A function that moves upward from left to right.
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inflection point
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Where the function changes from concave up to concave down or vice versa.
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instantaneous rate of change
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The rate of change (value of the derivative) at a particular moment.
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instantaneous velocity
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The rate at which an object is moving at a particular moment.
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inverse function
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A function obtained by switching the x and y variables in a function.
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left-hand limit
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The value that a function is approaching as x approaches a given value through values less than x
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l'hopital's rule
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Finding the derivative of the numerator and denominator to evaluate the limit of a function.
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limit
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The value that a function approaches as the domain variable approaches a specific value.
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limit at infinity
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Numerator is higher degree = does not exist. Numerator and denominator are same = division of coefficients. Denominator is higher degree = 0.
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local extrema
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A point where the graph has a peak or a valley.
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maximum
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The highest point on a graph.
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mean value
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The average of a set of numbers.
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mean value theorem
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f'(c)= f(b)-f(a)/b-a
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minimum
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The lowest point on a graph.
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monotonic
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A function that is only increasing or only decreasing.
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non-removable discontinuity
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A point at which a graph is connected.
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normal line
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The line perpendicular to a function.
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odd function
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A function with a graph that is symmetric with respect to the origin.
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one-to-one function
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Every number in the range corresponds to one number in the domain.
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open interval
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Does not include its endpoints.
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optimization
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A process that maximizes or minimizes some quantity to have the best fit.
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product rule
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(uv)= u'v + uv'
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quadratic formula
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-b±√b²-4ac / 2a
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quotient rule
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lo(hi') - hi(lo') / lo²
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range
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The set of y-values of a function.
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rate of change
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Slope of a function.
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related rates
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Rates of change are related by differentiation.
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relative minimum
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The lowest point in a particular section of the graph.
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relative maximum
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The highest point in a particular section of the graph.
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removable discontinuity
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Hole in the graph.
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right-hand limit
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The value that a function is approaching as x approaches a given value through values more than x
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right-hand sum
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A sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the right endpoint of the sub-interval.
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second derivative
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Gives points of inflection.
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second derivative test
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Determines whether the function is concave down, or neither at a point
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slope
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Change of steepness in a graph.
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speed
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Distance covered per unit of time.
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symmetry
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Having the same shape, size, and position on both sides of a dividing line.
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tangent line
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A line that touches a curve at a point without crossing the cure.
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unit circle
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A circle whose center is at the origin and has a radius of one.
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velocity
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The rate of change in the position of an object.
