Question

Can someone check my answer?
Attached below.

Answer 1

@aaronq

Answer 2

what's the derivative equal to?

Answer 3

ds/dt = t² - 12t + 36
t² - 12t + 36 > 0

Answer 4

what does t^2-12t+36 factor to?

Answer 5

(t - 6)² > 0

Answer 6

is it ever possible for (t-6)^2 to be negative?

Answer 7

I don't know. .-.

Answer 8

squaring any number makes it 0 or some positive number

it's impossible to square a real number and get a negative result

Answer 9

Oh. Okay.

Answer 10

so because (t-6)^2 is never negative, this means that s ' (t) is never negative and the particle NEVER moves to the left

Answer 11

it's always moving to the right with the exception that when it gets to t = 6, the particle stops moving completely

Answer 12

So would it be A?

Answer 13

well 0 < t < 6 is one interval while 6 < t < 15 is another

if they only allow you to choose one interval, then yeah it looks like it's A

Answer 14

Thank you!

Answer 15

choice D looks really compelling, but it's false when t = 6

you're welcome