Question

a particle moves along the y axis so that its position at any time t, for 0 is less than or equal to t which is less than or equal to 5, is given by y(t)=t^4-18t^2. in which intervals is the particle speeding up?

Answer 1

y'=4t^3-36t= 4t(t^2-9)=4t(t+3)(t-3)

y"=12t^2-36=12(t^2-3)=12(t+sqrt3)(t-sqrt3)

so when t=less than sqrt3, y"=+ *- or negagive, slowing down.
t= greater than sqrt3, y"=+ * + speeding up.