Vocabulary
Name at least one of the three terms used to describe f ' (x) AKA dy/dx
Derivative
Slope of Tangent Line
Instantaneous Rate of Change
This is the quotient rule
[vu' - uv']/[v2]
Is there a time interval during which R(t) = 80 must be true? If so, which one?
Yes, during the interval 5 < t < 10
On the open interval -8 < x < 6, these are the critical points of the graph of f
x = -6 and x = 2
f(x) has a critical point when f ' (x) = 0 or is undefined. When f ' (x) = 0, there is this additional special name.
Horizontal tangent
When finding the limit of a fraction, if both the numerator and denominator = 0, we should do this.
L'Hopital's rule
Take the derivatives (separately) and try again
Estimate R'(12). Include units.
R'(12) = -4 people per minute per minute
Does the graph of f have a point of inflection at x = 3? Explain.
Yes, because the graph of f '(x) = g(x) switches directions at x = 3
According to the _______, the average rate of change over an interval of a differentiable function must equal the instantaneous rate of change at some point within the interval.
Mean Value Theorem
To find a trapezoidal sum, do this.
Average together the left/right Riemann sums
Use a right Riemann sum with 3 subintervals to estimate the number of people who left the building in the 15 minutes.
5(100) + 5(75) + 5(55) = 500 + 375 + 275 = 1,150 people
This is f(0)
8 + 4pi
This is the first step in solving a differential equation, like dy/dx = (y - 1)x3
Separating the Variables
Evaluate the integral from 0 to 5 of R'(3t)
-15
Let h(x) = [g(x)] / [x2 + 1]. Find h'(1)
-3
[Use quotient rule: u = g(1) = 3; u' = g'(1) = -3; v = x2 + 1 = 2; v' = 2x = 2]