Note Cards For AP Test Flashcards
(34 cards)
What is a differential equation?
It is an equation that has a derivative in it.
What does d^2y/dx^2 mean?
Find the second derivative.
What is the integral of any rate of change?
The total change of the function from the lower limit to the upper limit.
What is the relationship between position, velocity, and acceleration?
Given position as s(t) its derivative is v(t) velocity, its second derivative or the derivative of velocity is a(t), acceleration. s’(t)= v(t)
s’‘(t)= v’(t) = a(t)
How do you find the instantaneous rate of change?
It is the slope at that point. Take the derivative and plug in your point.
What are critical points?
These are where the first derivative is zero or undefined. These are the candidates for the relative (local) max and mins.
How do you find position of a particle at time t?
Take the starting position and add it to the integral of the velocity, or of the rate of change.
How would you find the absolute max or min of a function?
Find and check all of the critical numbers. Put these into the original function along with the END POINTS to find the absolute extrema.
How do you tell if the speed of a function is increasing or decreasing?
When the velocity and acceleration have the same sign it is speeding up, otherwise it is slowing down.
How would you answer problems of the form:
Lim h➡️0 cos(x+h)-cos(x)/h
This is another way to ask for the derivative of the given function, cos(x)
Given the position function, how would you find the average velocity?
Take the slope of the end points. This will give you distance over time which is the average velocity.
How do you find the limit of a function as x approaches infinity?
Look at the degree of both the numerator and denominator. If the top has a larger degree the limit is infinity, if the bottom is bigger the limit is zero. If the degrees are the same make a fraction out of the leading coefficients.
How do you find the one-sided limits?
Find the y-value only from the one side. 5^+ would be from the right side of five, 5^- from the left side of five. These limits always exist.
How do you find the point of inflection of a function?
Find/look at the second derivative. The points of inflection are where the second derivative crosses the x-axis. The maxs and mins of the FIRST derivative will be inflection points of the original function.
How do you find the limit of a function as x approaches c?
Look to both the right and left of c. The y-value must be the same on both sides for the limit to exist. The limit is that y-value. You must state that both the right and left side limits are equal on the AP exam.
How do you find a tangent line?
Take the point of tangency and the slope by finding the derivative.
y-y1=m(x-x1) can be used.
Given an equation in factored form, how do you know which factors are tangent to the x-axis?
Factors with even exponents do not cross the x-axis.
f’(x)=(x-2)^2(x+3)^4 will only have a min at x=2 in the original function.
What is the mean value theorem?
The function MUST be differentiable on its domain. It states that if you take the slope of the end points there must be another domain with the same slope.
What is a linear approximation?
Using a tangent line to estimate values of your function.
How do you find the area between two curves?
Find their points of intersection, then integrate the top curve minus the bottom curve, or the right minus the left using y’s inside.
What is the result of switching the limits of integration?
It changes the sign of your answer when integrating.
What does “twice differentiable” mean?
Both the first and second derivative exist.
What does “orthogonal” mean?
Perpendicular, forming right angles.
What is a Riemann Sum?
The area under the curve usually found by using rectangles, the right, left, or midpoint.
