Any Calculus whizes out there? I could use some help on a problem from my calc book that isnt in the back....?

Question

If F(t) = 6+4e^-2t represents the demand price for a certain commodity, t is in months. Show that F(t) is decreasing on the interval and is concave upward on the interval. Please help...

Answer 1

F'(t) = -8e^(-2t) < 0 for all t, so it's decreasing on all intervals.

F''(t) = 16e^(-2t) > 0 for all t, so it's always concave up.

Answer 2

F´(t) = -8e^-2t .As the exponential is always positive F´is always negative and so F(x) is decreasing
F´´(t) =16 e^-2t and is positive so the concavity is upwards