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.

Answer 1

How about getting the second derivative?

Answer 2

Is this the equation?

\[6x^2 + \frac{x}{2} + 3 + \frac{6}{x}\]

Answer 3

yeah that's it

Answer 4

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

Answer 5

I thought it was just the first derivative?

Answer 6

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.

Answer 7

ohh ok. Thank you.