# Intervals

• Aug 9th 2009, 06:53 PM
dimanre
Intervals
I have the following problem

g""(x)=7x-2

Determine intervals on which original function is concave up and intervals on which it is down.

If someone could help me and tell me what the answer is, I would greatly appreciate it.
• Aug 9th 2009, 06:58 PM
Jhevon
Quote:

Originally Posted by dimanre
I have the following problem

g""(x)=7x-2

Determine intervals on which original function is concave up and intervals on which it is down.

If someone could help me and tell me what the answer is, I would greatly appreciate it.

are you sure you meant to type ""? that would be the 4th derivative
• Aug 9th 2009, 07:00 PM
dimanre
Thanks
No..I meant to type it as second dirivitive..thanks
• Aug 9th 2009, 07:03 PM
eXist
I'll help ya :D

To find where a function is concave up or concave down, you need to calculate the second derivative denoted $f''(x)$. In this case, they gave you it: $g''(x)=7x-2$

Now, once you calculate the second derivative, you look for the intervals where it is positive or negative. Where the second derivative f''(x) is positive, then the graph of f(x) is concave up. Where it is negative, the graph of f(x) is concave down :D.

Now find those intervals :D
• Aug 9th 2009, 07:05 PM
dimanre
ok
So do you plug in random numbers to test it? and if so, can you show an example?
• Aug 9th 2009, 07:08 PM
eXist
Well you find the zeroes of that function. Then test points to the left and right.
• Aug 9th 2009, 07:16 PM
dimanre
Got it..thanks
Thanks for your help, I really appreciate it.