# Need help on this curve-sketching problem.

1. Feb 26, 2005

### jzq

Would someone please help me on this problem? I'm sorry if it is hard to read. I'm new to this forum and haven't had the time to read over the latex system guide. I just need to make sure the information that I got is correct. Thank you.

Sketch the graph of the function, using the curve-sketching guide.

Function: f(t)=3(t)^(4) + 4(t)^(3)

From this function, I derived this information (Please check):
Domain: all real #s
x-int: (0,0)
y-int: (0,0)
Asymptote: none
End Behavior: points up at both ends.
First Derivative: f'(t)=12(t)^(3) + 12(t)^(2)
Decreasing: (-infinity,-1)
Increasing: (-1,+infinity)
Relative Minima: (-1,-1)
This is where I think I messed up!
Second Derivative: f''(t)=36(t)^(2) + 24(t)
Concave Up: (0,+infinity), (-infinity,-2/3)
Concave Down: (-2/3,0)
Points of Inflection: (0,0), (-2/3,-16/27)

Last edited: Feb 26, 2005
2. Feb 26, 2005

### Jameson

Perfect. Got the same thing.

EDIT: You missed one x-intercept at x = -4/3. Besides that, looks good.

3. Feb 26, 2005

### jzq

Thanks alot!!!