What are the relative extrema of this equation? x^4 - 2x^3
2 Answers
Local minimum at
Explanation:
To find local extrema, we use the first an second derivative tests.
For the sake of the first derivative test, let's factor this to:
If we set
Now we use the second derivative test to determine minimum/maximum/point of inflection:
Factoring, we get
Now we evaluate our two possible extrema using the second derivative test:
All of this can be observed on the graph of the original function:
graph{x^4-2x^3 [-1.49, 4.67, -1.958, 1.122]}
We have a local minimum at
Explanation:
Determine
We have prospective extrema at
At each of these intervals, we want to determine if
We have an extremum at any
Let's select
Let's select
Let's select
To determine the
We have a local minimum at