Refer to the table below if needed.
2 answers:
You might be interested in
Answer:
See below
Step-by-step explanation:
Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.
Let's do as an example
By using the power rule where , then
Now set and solve for
:
By plugging our critical points into , we can see that our extreme values are located at
,
, and
.
The second derivative would be and plugging in our critical points will tell us if they are minimums or maximums.
If , it's a minimum, but if
, it's a maximum.
Since then
is a local maximum
Since , then
is a local minimum
Since , then
is a global minimum
Therefore, the extreme values of are a global minimum of
, a local minimum of
, and a local maximum of
.
Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.
