Question

HELP PLEASE !
A spring is moving up and down according to the function s(t) = -4cos(t).
Part a) Find the first derivative and calculate the velocity of the spring at t = 3pi/4
Part b) Is the spring moving upward or downward at this point? Justify your answer.

Answer 1

differentiate the function with respect to t:
(d/dt) -4cos(t) = -4 sin (t)
then plug in the value t=3pi/4 in your new function

Answer 2

the function you have at first gives you the position of the spring at any time
the first derivative gives you the velocity of the spring at any time so once you plug in the time value, the sign of the answer tells you what the direction of motion is