Interpreting Sign Chart of a Polynomial, the First Derivative, and the Second Derivative

After finding the sign chart for your polynomial, first, and second derivatives you may lose sight of what they all represent.

The sign chart of your polynomial will tell you when your function value, f(x), is above (positive on sign chart) or below (negative on sign chart) the x-axis.

The sign chart of your first derivative tells you when your function is increasing (positive on first derivative sign chart) or decreasing (negative on first derivative sign chart).

The sign chart of your second derivative tells you when your function is concave up (positive on second derivative sign chart) or concave down (negative on second derivative sign chart).


0:00 Introduction
0:25 Interpreting the Polynomial Function Sign Chart
1:54 Interpreting the First Derivative Sign Chart
3:28 Interpreting the Second Derivative Sign Chart
4:30 Four possible combinations of First and Second Derivative Sign Chart patterns
4:42 Making sense of all three sign charts together
7:12 Using the template found using the sign charts in unison with graph of polynomial


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