Step 1

Compute dy/dx and d²y/dx².

Step 2

Find all points where dy/dx = 0 and all points where d²y/dx² = 0.

Step 3

Pick a few points

a = x₀, x_l, x₂, ..., x_n = b

in the interval [a, b]. They should include both endpoints, all points where the first or second derivative is zero, and at least one point between any two consecutive zeros of dy/dx or d²y/dx².

Step 4

At each of the points x₀, ..., x_n, compute the values of y and dy/dx and determine the sign of d²y/dx². Make a table.

Step 5

From the table draw conclusions about where y is increasing or decreasing, where y has a local maximum or minimum, where the curve is concave upward or downward, and where it has a point of inflection. Use Theorems 1-3 of this section and the tests for maxima and minima.

Step 6

Plot the values of y and indicate slopes from the table. Then connect them with a smooth curve which agrees with the conclusions of Step 5.