derivatives question story

Given the function http://www.imathas.com/cgi-bin/mimet...B360%7D%7Bx%7D, find the first derivative, http://www.imathas.com/cgi-bin/mimet...%5Cright%29%7D.

http://www.imathas.com/cgi-bin/mimet...right%29%7D%3D

Notice that http://www.imathas.com/cgi-bin/mimet...9%7D%3D%7B0%7D when http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D, that is, http://www.imathas.com/cgi-bin/mimet...9%7D%3D%7B0%7D.

Now, we want to know whether there is a local minimum or local maximum at http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D, so we will use the second derivative test.

Find the second derivative, *g"*http://www.imathas.com/cgi-bin/mimet...%5Cright%29%7D.

*g"*http://www.imathas.com/cgi-bin/mimet...right%29%7D%3D

Evaluate *g"*http://www.imathas.com/cgi-bin/mimet...%5Cright%29%7D.

*g"*http://www.imathas.com/cgi-bin/mimet...right%29%7D%3D

Based on the sign of this number, does this mean the graph of http://www.imathas.com/cgi-bin/mimet...ht%29%7D%7D%7D is __concave up__ or __concave down__ at http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D?

[Answer either **up** or **down** -- watch your spelling!!]

At http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D the graph of http://www.imathas.com/cgi-bin/mimet...ht%29%7D%7D%7D is concave

Based on the concavity of http://www.imathas.com/cgi-bin/mimet...ht%29%7D%7D%7D at http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D, does this mean that there is a __local minimum__ or __local maximum__ at http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D?

[Answer either **minimum** or **maximum** -- watch your spelling!!]

At http://www.imathas.com/cgi-bin/mimet...x%7D%3D%7B5%7D there is a local Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c

Be sure your variables match those in the question

Box 2: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c

Be sure your variables match those in the question

Box 3: Enter your answer as a whole or decimal number. Examples: 3, -4, 5.5

Enter DNE for Does Not Exist, oo for Infinity

Box 4: Enter your answer as letters. Examples: A B C, linear, a cat

Box 5: Enter your answer as letters. Examples: A B C, linear, a cat

Re: derivatives question story

what have you done with this problem?