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