Question

Finding when the function concaves upwards?

Answer 1

I keep getting it wrong lol

Answer 2

Set your second derivative equal to 0 and solve for x.

Answer 3

e^(-3t) is always going to be positive for any value of t

so focus on the (2t-3) portion

Answer 4

Then you need to test points to the left and right of your zeroes.

Answer 5

positive when t>=2

Answer 6

let g(t) be the second derivative function

g(t) = e^(-3t)*(2t-3)

you want to solve for t when g(t) > 0

Answer 7

g(t) > 0
e^(-3t)*(2t-3) > 0
2t - 3 > 0


I'm sure you see what to do next?

Answer 8

3/2

Answer 9

or 1.5, yes

Answer 10

t>3/2

Answer 11

:)

Answer 12

keep in mind that you will not be using a square bracket because you don't want to include t = 3/2 = 1.5

Answer 13

oh yeah, that makes the whole thing zero

Answer 14

correct which may mean it's at an inflection point

Answer 15

thanks :)

Answer 16

no problem