Section 1
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Local/Relative Minimum
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Last updated
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Date created
Mar 1, 2020
Cards (75)
Section 1
(50 cards)
Local/Relative Minimum
A point on the graph of a function where no other nearby points have a lesser y-coordinate.
Quotient Rule
Product Rule
g(x) is concave up
g''(x) is positive
Total Distance
Total distance traveled to do this calculate integral of velocity graph positive and negative sections separately and add absolute value of those together.
g(x) changes directions
g'(x) passes through 0
Local/Relative Maximum
A point on the graph of a function where no other nearby points have a greater y-coordinate.
g(x) is increasing
g'(x) is positive
Particular Solution
Integration that has value for c solved for by plugging in a known coordinate pair
U-Substitution
g(x) is concave down
g''(x) is negative
Trapezoidal Sums
Riemann Sums done with averaging two points instead of picking a side can be more accurate
Euler's Method
a method of approximation helpful when dy/dx has x and y terms in it
Area Between Curves
with f(x) on top and g(x) on bottom a and b represent bounds or where the two graphs intersect
g(x) has a point of inflection
g''(x) passes through 0 or DNE
Chain Rule
also applies to Trig functions, natural logs, and e
Stationary Points
Maximum Points, Minimum Points, and Points of Inflection
Disc Method of Rotation
V = pi * int from a to b of R(x)^2 dx R(x) is radius and dx is height rotated around variable inside
Area Under the Curve
Integral or antiderivative
Critical Point
Occurs when f'(x) = 0 Can be a min, max, or neither
Slope Fields
Drawing the slopes at different points for a function (often that is difficult to integrate) can help predict the shape of the function
Absolute Minimum
The lowest point of the function Needs to be proved with critical points and the limits as x approaches - infinity and + infinity
Slope
Rise over run
Partial Fractions
Splitting up a fraction into its parts can make integration easier!
L'Hopital's Rule
if lim x --> of g(x)/f(x) is 0/0 then you can derive
Continuity
A function is uninterrupted, this implies integratibility
Instantaneous Rate of Change
the rate of change at a particular moment, for F(x) this would be F'(x)
Velocity
The speed at which an object is traveling velocity function is the derivative of a position function in relation to time.
Definition of A Derivative
we say that f is differentiable at x = a and the limit is the derivative of f(x) at x = a, denoted by f prime of a.
Slowing Down
Acceleration has the opposite sign as Velocity
Displacement
The distance and direction of an object's change in position from the starting point. function is given in relation to time
Related Rates
A class of problems in which rates of change are related by means of differentiation. Standard examples include water dripping from a cone-shaped tank and a man's shadow lengthening as he walks away from a street lamp.
Mean Value Theorem
the average value on a certain integral must have a value of x that it is equal to
g(x) is decreasing
g'(x) is negative
Shell Method of Rotation
V = 2pi int from a to b of ( x F(x) ) dx rotated around opposite variable inside
Absolute Maximum
The y-value of a point on a graph that is higher than any of the other points on the entire graph. Needs to be proved with critical points and the limits as x approaches - infinity and + infinity
Linear Approximation
Using the tangent line to approximate nearby values
Intermediate Value Theorem
2nd Fundamental Theorem of Calc
d/dx (int from c to x of f(t) dt) = f(x)
Tangent Line
Straight line on the curve at a given point that can be used to estimate values near by
Integration by Parts
int u dv = u v - int v du
1st Fundamental Theorem of Calc
int from a to b of f'(x) dx = f(b) - f(a)
Washer Method of Rotation
V = pi * int from a to b of ( R(x)^2 - r(x) ^2 ) dx R(x) is furthest away from axis r(x) is closest to axis rotated around variable inside
Average Value
finds the average value of a function. often related to the mean value theorem
Find int 0 to infinity of f(x) dx
substitute b and do lim as b--> infinity
Extreme Value Theorem
Acceleration
The rate at which velocity changes Acceleration function is the derivative of a velocity function in relation to time
Riemann Sums
A Riemann Sum is a method for approximating integrals
Average Rate of Change
the change in the value of a quantity divided by the elapsed time
Speeding Up
Acceleration has the same sign as Velocity
Section 2
(25 cards)