# Thread: Graph Polynomial question

1. ## Graph Polynomial question

2. Originally Posted by colaname
For a & b,
Take the derivative of your function and set it equal to zero. Solve for x to tell you where the graph of the derivative intersects with the x axis. These are your critical values. You need to set up a number line and do a sign analysis with numbers to te left and right of your critical values. Plug those test values into your derivative. If your test values change from negative to positive, then f(x) is changing from increasing to decreasing, or vice versa, at those values. This will also tell you where you have min/max values.

So, to find where f(x) is increasing or decreasing, you need to find where f'(x)=0

For c & d,
concavity and inflection points are found with the second derivative. So, find your second derivative. Set is equal to zero solve for x. Set up another sign chart and use test values to find where the sign changes from - to + for the second derivative. When you have a sign change, this shows you where the original function changes in concavity. *Concave up, tangent line is below the function, concave down the tangent line is above the function. Inflection points are the points where the concavity changes.