Question

1. A baby is being bounced approximately according to the position function 10*sin(2*pi*t/2) (distance in centimeters, t in seconds). Compute the acceleration function and report the maximum acceleration experienced.





2. What x value minimizes x/5 + 3/x , when x>0 ? Express it precisely, not just its decimal version (so, just asking your calculator to minimize it won’t be sufficient)

Answer 1

#1. If y = a sin(bx), then
y' = ab cos(bx)
y" = -ab^2 sin(bx)
and what's with the 2*pi/2 ? Why not just say pi?
and, of course, max acceleration is where -ab^3 cos(bx) = 0
That will be at the max or min of the graph for y(x), since that is where the curvature is greatest.

#2. y = x/5 + 3/x
y' = 1/5 - 3/x^2 = (x^2-15)/(5x^2)
so, where is that zero?
Be sure to check that it's the minimum, not the maximum.
check your work at some handy online graphing site.

Answer 2

so every even t is a full period?