3.4 Derivatives as rates of change; Question 150

[Eigenvalue]

The given function represents the position of a particle traveling along a horizontal line. Find the velocity and acceleration functions; determine when the object is slowing down or speeding up

s(t)=2t³-3t²-12t+8

[Eigenvalue]

a) Velocity is the derivative of position
Take the derivative of both sides of s(t):
v(t)=(s(t))'=(2t³-3t²-12t+8)'
v(t)=6t²-6t-12

b) Acceleration is the derivative of velocity
Take the derivative of both sides of v(t)
a(t)=(v(t))'=(s(t))"=(6t²-6t-12)'=12t-6

[Eigenvalue]

Note: I have yet to do part C, but it will be posted tomorrow.