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.

Question

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.

anonymous · Answer

How about getting the second derivative?

amistre64 · Answer

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

anonymous · Answer

yeah that's it

anonymous · Answer

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

anonymous · Answer

I thought it was just the first derivative?

anonymous · Answer

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.

anonymous · Answer

ohh ok. Thank you.