calc question?

Question

The displacement from the origin of a particle moving on a line is given by
s = t^4 – 4t^2. The maximum displacement during the time interval -2 < t < 4 is? I keep getting ridicoulous answers if i use the globals so please help

Answer 1

Take the derivative of s with respect to t, and set that equal to zero, and whatever equation comes out of that will tell you when the displacement is either at a local high point or local low point, then test the value of s at the local high/low, and at the end points to see which value is the highest, and that's your answer.

s' = 4t^3 - 8t = 0
4t(t^2 - 2) = 0
t = 0, sqrt(2), -sqrt(2)
At t = 0, s = 0^4 - 4*0^2 = 0
At t = sqrt(2), s = 4 - 8 = -4
At t = -sqrt(2), s = -4
Check endpoints:
At t = -2, s = 16 - 16 = 0
At t = 4, s = 256 - 64 = 192

I guess the maximum displacement is at the end of the interval at t = 4 (or just before 4 if you can't include 4).

Answer 2

If you suppose s>=0
s =t^2*abs(t^2-4) = t^2 * (t2-4) if t>2 or t<-2
s =t^2*(4-t^2)

The first case gives NO maximum
In the secon case
ds/dt = 8t -4t^3 = 4t( 2 -t^2) =0 t=0,-sqrt2 ,sqrt2

You get maximums at t= -sqrt2 and +sqrt2 with d= 4

Answer 3

¿?