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"

Evaluateg".

g"

Based on the sign of this number, does this mean the graph of isconcave uporconcave downat ?

[Answer eitherupordown-- watch your spelling!!]

At the graph of is concave

Based on the concavity of at , does this mean that there is alocal minimumorlocal maximumat ?

[Answer eitherminimumormaximum-- 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