Question

an object is moving along the x-axis such that the position of the object in masters at time t in seconds is giving by the function x(t)=t^3-12t^2+36t-5, for 0<=t<=8


a- when is the object moving right? and when to the left?

b- When is the object's velocity both positive and increasing

c- When is the object's velocity both negative and decreasing

d- You may notice the object starts 5m from the origin, but when is it furthest from the origin?

e- It can be shown that x(t)>0 when 0<=t<=8. When is the object closet to the origin?

f-Sketch a graph of x(t)

Answer 1

moving right ==> distance increasing
x increasing ==> dx/dt > 0

Now see what you can do with the questions. There are lots of online graphing web sites that you can use to confirm your graph ideas. (desmos, wolframalpha, ...)