# Help with Concavity

• Nov 21st 2012, 03:46 PM
lguto
Help with Concavity
Hi guys, so I'm having trouble with the following question:

http://img855.imageshack.us/img855/9...mttulo1wrl.png

For f'(x), I got 2x and for f"(x) I got 2...

I need the values for which f"(x)=0, but how can I find it then f"(x)=2? I couldn't find any similar examples on Google guys, please help.

Cheers
• Nov 21st 2012, 04:06 PM
skeeter
Re: Help with Concavity
the graph of $f(x) = x^2 - 49$ is a parabola that opens upward.

$f''(x) = 2 > 0$ says the graph of $f(x)$ is concave up everywhere.
• Nov 21st 2012, 04:07 PM
Plato
Re: Help with Concavity
Quote:

Originally Posted by lguto
Hi guys, so I'm having trouble with the following question:

http://img855.imageshack.us/img855/9...mttulo1wrl.png

All you need to do is find where $f"(x)>0$.
• Nov 21st 2012, 04:09 PM
lguto
Re: Help with Concavity
Quote:

Originally Posted by skeeter
the graph of $f(x) = x^2 - 49$ is a parabola that opens upward.

$f''(x) = 2 > 0$ says the graph of $f(x)$ is concave up everywhere.

Theres an interval where f(x) is concave down, but I cant seem to find it also...

I tought it would never be concave down...

You can say that is concave up everywhere just because 2 > 0?

EDIT:

For A), the interval is (-inf,inf), but B) insists that there's still an interview where the function is concave down... I dont understand how is that possible since it is concave up everywhere...
• Nov 21st 2012, 04:29 PM
skeeter
Re: Help with Concavity
There is no interval where $f(x) = x^2 - 49$ is concave down. Some advice ...

(1) LOOK at the graph of $f(x) = x^2 - 49$. Frankly, I'm surprised that a calculus student cannot sketch this simple graph from memory.

(2) Review your notes/text over what the sign of $f''(x)$ says about the graph of $f(x)$.
• Nov 21st 2012, 04:32 PM
lguto
Re: Help with Concavity
Quote:

Originally Posted by skeeter
There is no interval where $f(x) = x^2 - 49$ is concave down. Some advice ...

(1) LOOK at the graph of $f(x) = x^2 - 49$. Frankly, I'm surprised that a calculus student cannot sketch this simple graph from memory.

(2) Review your notes/text over what the sign of $f''(x)$ says about the graph of $f(x)$.

I got the interval where it is concave up. I could sketch this graph and find the interval thanks to your help. But the question still asks for an interval where the function is concave down. its not cocave down anywhere, but it wont accept my answer. Ive tried to put "none" or "0" and it doesnt work... Maybe a problem with the website?

Thanks mate!
• Nov 21st 2012, 04:39 PM
MarkFL
Re: Help with Concavity
Since the second derivative is positive for all real x, then the function is concave up for all real x. I can't help with what to enter though, since I went to school in the dark ages where a professor actually manually graded homework that was turned in by hand. :)