PVA Flashcards
Position
f(x)
y(x)
Velocity
y ‘(x)
position-time graph
Acceleration
y ‘‘(x)
Positive velocity
moving up/forward/right
Negative velocity
moving down/backward/left
Zero velocity
not moving/ “at rest”
Instantaneous velocity
dy/dt
v(t)
y ‘(t)
Positive acceleration
Increasing velocity
Negative acceleration
Decreasing velocity
Zero acceleration
horizontal tangent line
Average acceleration
(delta V) / (delta t)
Instantaneous acceleration
dV/dt
v ‘(t)
y ‘‘(t)
Speed increases when…
Velocity and acceleration are both positive or both negative
Speed decreases when…
Velocity is positive while acceleration is negative (or vise versa)
First derivative test
f ‘(x) changes
relative minimum (- to +)
relative maximum (+ to -)
Second derivative test
If second test fails, try first
relative minimum: f ‘(a) = 0 and f ‘‘(x) > 0
relative maximum: f ‘(a) = 0 and f ‘‘(x) < 0
Implicit differentiation
EXAMPLE)
y^2 + 4y = 4x^3
2y(dy/dx) + 4(dy/dx) = 12x^2
dy/dx (2y + 4) = 12x^2
dy/dx = (12x^2) / (2y + 4)
