Calculus Help?

Question

I'm stuck:

"Find the intervals in which the function is increasing and decreasing"

g(t) = -3t^2 + 9t + 5

Any help would be awesome!

Answer 1

increasing when t < 3/2
decreasing when t > 3/2

It increases when the derivative is positive and decreases when it is negative.

g'(t) = -6t + 9

Answer 2

Hi,
The graph of your function is, of course, a parabola that opens downward. So, the function is increassing (g(t) gets larger) to the left of the vertex and decreasing to the right of the vertex. The vertex is at t = 3/2.
To find the vertex, in case your are interested, you can do one of two things:
1) Use the formula t = -b/2a. (From the formula ax² +bx +c).
2) If you know calculus you can take the derivative and set it equal to zero; then solve for t.
-6t +9 = 0
t = 3/2

FE