POS; VEL; ACCEL

Position

s(t); x(t)

Velocity

v(t); s’(t); x’(t)

Speed

|v(t)|; |s’(t)|; |x’(t)|

Acceleration

a(t); v’(t); s’’(t); x’’(t)

Distance

Calculate changes in direction from start to end—>add up pos.

|x(b)-x(a)|

Displacement

s(b)-s(a)

Average velocity

s(b)-s(a) / b-a

Average speed

|s(b)-s(a) / b-a|

Average acceleration

v(b)-v(a) / b-a

When is a function increasing?

f’(x)>0

When is a function decreasing?

f’(x)<0

When does a function have critical values at x?

f’(x)=0/DNE

How do you determine a relative maximum?

f’(x)=0/DNE & f’(x) sign goes from + —> -

OR

f’’(x)<0

How do you determine a relative minimum?

f’(x)=0/DNE & f’(x) sign goes from - —> +

OR

f’’(x)>0

When is a function concave up?

f’’(x)>0

When is a function concave down?

f’’(x)<0

When does a function have a point of inflection?

f’’(x)=0 & f’’(x) sign changes