## anonymous 5 years ago What are all the values of x for which the graph of y=6x^2+x/2+3+6/x is concave downward? I get the derivative but when i solve for x i don't get the answer.

1. anonymous

How about getting the second derivative?

2. amistre64

Is this the equation? $6x^2 + \frac{x}{2} + 3 + \frac{6}{x}$

3. anonymous

yeah that's it

4. anonymous

Concave up, down...we need to evaluate second derivative also.

5. anonymous

I thought it was just the first derivative?

6. anonymous

You can, but second tells you immediately without any inspection: if 2nd der is positive over interval concave up, if negative over interval concave down. It is one of your tools.

7. anonymous

ohh ok. Thank you.