Section 1
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How do you find the maximum height of an object?
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Date created
Mar 1, 2020
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Section 1
(62 cards)
How do you find the maximum height of an object?
Set the velocity function to zero, solve for the time, then plug it into the position function.
How do you find the zeros of f(x)?
Set the function equal to zero. Factor or use the quadratic formula if quadratic. Graph to find the zeros on calculator.
How do you find the velocity of an object when it hits the ground?
Set the position function to zero, solve for the time, then plug it into the velocity function.
How do you know that f(x) is even?
Show that f(-x) = f(x). This shows that the graph of f is symmetric to the y-axis.
How do you factor a sum or difference of cubes?
What is the justification for where a function is increasing?
This is where f'(x) > 0
How do you find the limit of f(x) as x approaches + or - infinity?
How do you justify intervals where the velocity of an object is positive?
It is where the position ( s(t) ) is increasing, or where s'(t) is positive.
What is the justification for relative max/min using the second derivative test?
How do you justify intervals where the acceleration of an object is negative?
It is where the velocity ( v(t) ) is decreasing, or where v'(t) is negative.
What is the justification for a point of inflection?
What is the derivative of csc(u)?
How do you tell if the speed of a particle is decreasing at a particular time?
You show that the velocity and acceleration have different signs at that time.
What is the justification for when a particle is moving right?
This is when v(t) > 0
What are the two definitions of the derivative?
What is the derivative of tan(u)?
What is the derivative of sec(u)?
How do you justify intervals where the velocity of an object is negative?
It is where the position ( s(t) ) is decreasing, or where s'(t) is negative.
What is the derivative of sin(u)?
ln(a^b)
What is the derivative of ln(u)?
What is the justification for where a function is concave up?
This is where f"(x) > 0
What is the Mean Value Theorem (MVT)?
How do you find the instantaneous rate of change of the function f at x = a?
Find the slope of the tangent line to the function f at x = a. Or, find the derivative of the function at a. Or, find f' (a)
How do you justify intervals where the acceleration of an object is positive?
It is where the velocity ( v(t) ) is increasing, or where v'(t) is positive.
What is the justification for where a function is decreasing?
This is where f'(x) < 0
What is the justification for when a particle is moving left?
This is when v(t) < 0
How do you find the vertical asymptotes of f(x)?
Express f(x) as a fraction, express numerator and denominator in factored form, and do any cancellations. Set denominator equal to 0.
What is Roll's Theorem?
What is the derivative of e^u?
What is the derivative of cos(u)?
What is the justification for when a particle is speeding up?
This is when v(t) and a(t) have the same sign.
What is the derivative of cot(u)?
How do you find horizontal asymptotes of f(x) algebraically?
Find the limit if f(x) as x approaches + and - infinity.
What is the Intermediate Value Theorem (IVT)?
How do you show that f(x) is odd?
Show that f(-x) = -f(x). This shows that the graph of f is symmetric to the origin.
ln(a x b)
ln(a) + ln(b)
What is the integral of 1/u?
ln(a/b) =
ln(a)-ln(b)
How do you find the average rate of change of the function f on [a,b]?
How do you find the domain of f(x)?
Assume domain is (−∞,∞). Restrict domains: denominators ≠ 0, square roots of only non-negative numbers, logarithm or natural log of only positive numbers.
How do you find the equation of line normal to a graph at x = c?
Find the slope of the tangent line to the graph at x = c, then use the opposite reciprocal slope to write an equation.
How do you show that f(x) is continuous at x = c?
How do you find vertical asymptotes of f(x) algebraically?
Find where the function is undefined. This is usually where the denominator of f(x) = 0.
What is the justification for a critical number?
This is where f'(x) = 0, or f'(x) is undefined.
What is the justification for relative max/min using the first derivative test?
What is the justification for where a function is concave down?
This is where f"(x) < 0
How do you tell if the speed of a particle is increasing at a particular time?
You show that the velocity and acceleration have the same sign at that time.
What is the justification for when a particle is slowing down?
This is when v(t) and a(t) have different signs.
What is the derivative of a^u?
Section 2
(28 cards)