Asymptotes and Limits of Infinity

Directions: sketch the graph.

f(t) = 3t^4 - 4t^2 + 3

This is the first problem I've had like this. Since the polynominal equation isn't obvious, I think I take x to the limit of infinity:

f(t) 3t^4 - 4t^2 +3 = 3t^2 -4 +3/t^2 = 3t^2 = 0

lim approaches infinity +

t=0

f(0) = 3

extrema point at (0,3)

f'(t) = 12t^3 - 8t

f'(t) = 4t(3t^2 - 2)

f'(t) = 4t =0

f'(t) = t=0

f'(t) = 3t^2 -2 = 0

f'(t) = 3t^2 = 2

f'(t) = t^2 = 2/3

f'(t) = t = 2/3

f'(t) = 0.8164

f'(.8164) = 12(.8164)^3 - 8(.8164)

f'(.8164) = .6529 - 6.5312

f'(.8164) = -5.8783

critical points at (0,0) and (.8164, -5.8783)

f"(t) = 36t^2 - 8

f"(t) = 4(6t^2 - 2)

f"(t) = 4

f"(t) = 6t^2 - 2 = 0

f"(t) = 6t^2 = 2

f"(t) = t^2 = 1/3

f"(t) = t = 1/3

f"(t) = t =.577350269

f"(4) = 36(16) - 8

f"(4) = 568

(4,568)

f"(.577350268) = 36(.577350269)^2 - 8

f"(.577350269) = 12 - 8

f"(.577350269) = 4

(.577350269,4)

relative maximium (4,568)

Anything I am forgetting (or just plain wrong)?