(0, 0). Note also that the function is positive for x < 0 and negative for x > 0, so the curve is
increasing for x < 0 and decreasing for x > 0. Next, we take the second derivative: =
= . If we set this equal to zero, we getno solution, which means that there is no point of inflection at the origin. Notice that the second
derivative is positive for x < −2, negative for −2 < x < 2, and positive for x > 2. Therefore, the
curve is concave up for x < −2 and x > 2, and concave down for −2 < x < 2. Next, we need to
determine if each critical point is maximum, minimum, or something else. If we plug x = 0 into
the second derivative, the value is negative, so (0, 0) is a maximum. Now, we can draw the
curve. It looks like the following: