Question

Can someone help me with this Calculus problem?

Answer 1

This particle can transport instantaneously.. as it approaches t=2 it is at -1 and suddenly appears at +2 at t=1.

Answer 2

And for part B... as x = -1 f(x) approaches infinity?

Answer 3

Well for part a)

At t=-1s - It starts at y=-2 and it looks like at rest...then accelerates as it approaches t=1s when just before t=1s it is at location y=-1, then suddenly teleports and appears at y=2 at exactly t=1s. From there it is initially moving pretty fast and decelerates until reaching t=2.

Answer 4

If anything isn't clear let me know

Answer 5

Got the idea...but how do we know that it is "at rest" at y = -2?

Answer 6

well it cant be said for sure, the tangent cant be there on an endpoint, the velocity is the slope of the tangent at any point on the curve...
I just say "rest" because it looks like that would have a horizontal tangent, or for sure a veryu very small sloped tangent just after t=-1

Answer 7

Okay...what else can be said about the graph?

Answer 8

For b) as time goes on forever to infinity, it doesnt move

Answer 9

It looks like the graph levels out horizontal after t=4, so i would say the particle slows down as it approaches t=4 and stops at y=1

Answer 10

The intermediate value theorem requires the graph to be Continuous, so you can't use that for those intervals

Answer 11

But the portion on the left is continuous, and there is a zero on the interval

Answer 12

Can we choose two points on the interval and show that the graph has to cross the x-axis at some point?

Answer 13

on [-3 , 0] the thing is not continuous. It looks like it goes off to infinity, or keeps speeding up, then suddenly it is at y=-1

Answer 14

okay...so it's not possible in the second interval either?

Answer 15

No on [0,3] time, the function is not continuous at t=1,