Question

The position of a leaf as it floats along a river is given by the function s(x) = x^3 - sinx, where s(x) is in meters and x is time in seconds.

- Find the acceleration of the leaf at 2pi seconds.

- Is the leaf moving in its original direction or in the opposite direction that it was originally moving?
Leave all solutions in exact form.

(please show the steps if you can, so i can follow)

Answer 1

"The position of a leaf " , relative to what ?

anyway ....

s(x) = x^3 - sinx
v(x) = 3x^2 - cosx
a(x) = 6x + sinx
so when x = 2π
a(2π) = 12π + sin(2π) = 12π + 0 = 12π

Answer 2

v(0) = -1 < 0

v(2π) = 12π^2 - 1 > 0
so it is now moving in the opposite direction