midterm review Flashcards
manifesting a >80 on this test !
at rest, v(t) = ?
v(t) = 0
particle moving RIGHT (forward or up)
v(t) > 0 or positive
particle moving LEFT (backward or down)
v(t)<0 or negative
avg. velocity on [a, b]
(1/b-a) ∫ b to a v(t) dt
or x(b) - x(a) / b - a
instantaneous velocity @ time t = a
v(a) = x’(a)
acceleration at time t = c
a(c) = v’(c) = x’‘(c)
velocity increasing
a(t) > 0 or POS
velocity decreasing
a(t) < 0 or NEG
speed =
v(t)|
absolute value of v(t)
speed increasing
v(b) and a(b) have SAME signs
both velocity and acceleration are pos/neg
speed decreasing
v(b) and a(b) have opposite signs
velocity and acceleration are pos & neg or vice versa
total distance traveled on [a, b]
∫b to a of abs. value v(t) dt
b on top of integral, and a on bottom
net distance traveled
∫ b to a of v(t) dt
b on top, a on bottom (of integral)
position of object at time t=b
x(b) = x(a) + ∫ b to a v(t) dt
b on top, a on bottom (of integral)
particle is farthest left or right ?
compare positions (x-values) @ endpoints & @ local min/max
velocity at t = b ?
v(b) = v(a) + ∫b to a of a(t) dt
b on top, a on bottom (of integral)
moving away or towards origin at t = b ?
AWAY = x(b) & v(b) have SAME signs
TOWARDS = x(b) & v(b) have OPPOSITE signs
particle moving away or towards each other
determine each particle’s position and velocity, make sktech and compute.
average VALUE of a function, f(x) on [a, b]
1/b -a ∫b to a of f(x) dx
b on top, a on bottom (of integral)
average RATE of f(x) on [a, b]
f(b) - f(a) / b - a
or
1/b-a ∫b to a of f PRIME of x dx
b on botom, a on top of integral
slope of position = ?
velocity
so x’(t) = v(t)
slope of velocity = ?
acceleration
so v’(t) = a(t)
during what intervals is the particle moving left ?
left -> v(t) < 0
during what intervals is the particle moving right ?
right -> v(t) > 0
during what intervals is the particle’s acceleration positive ?
a(t) > 0
during what intervals is the particle’s acceleration negative ?
a(t) < 0
when is speed increasing ?
velocity and slope of velocity (or acceleration) have SAME signs
when is speed decreasing ?
velocity and slope of velocity (acceleration) have OPPOSITE signs
critical point
where the derivative of the function changes signs
relative max = ?
(think about f’(x) )
when f’(x) changes from POS (inc.) to NEG (dec.)
relative min = ?
(think about f’(x) )
when f’(x) changes from NEG (dec.) to POS (inc.)
when is f increasing ?
(given f(x) & f’(x))
where f’(x) is POS or f’ > 0
when is f decreasing ?
(given f(x) & f’(x))
where f’(x) is NEG or f’ < 0
when is f concave up
(given f ‘‘(x) )
f’’> 0
when is f concave down
(given f’‘(x) )
f’’ < 0
where is a POI ?
(using f’’)
x values that f’’ changes signs at
