The function f(x) = 4t^3 - 57t^2 + 210t + 6 is the vertical location of an object where f is in ft and t is in sec.

• Solve for an expression for the object's velocity.
• Solve for an expression for the object's acceleration.
• Solve for an expression for the object's speed.
• Solve for its displacement during the beginning five secs.
• Solve for its average velocity during the beginning five secs.
• Solve for the instantaneous velocity where time is 2.
• Solve for the acceleration of the object where time is 2.
• For which values will the object change direction?
• Solve for the acceleration each time the object changes direction.
• Solve for the speed of the object when time is 3 secs.
• Solve for the total distance the object travels over the beginning ten secs.