Thread: derivatives question story

Given the function , find the first derivative, .






Notice that when , that is, .

Now, we want to know whether there is a local minimum or local maximum at , so we will use the second derivative test.
Find the second derivative, g".
g"





Evaluate g".
g"

Based on the sign of this number, does this mean the graph of is concave up or concave down at ?
[Answer either up or down -- watch your spelling!!]
At the graph of is concave

Based on the concavity of at , does this mean that there is a local minimum or local maximum at ?
[Answer either minimum or maximum -- watch your spelling!!]
At 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

what have you done with this problem?