When x = 0, y = 0When x = , y = 1When x = − , y = 1Thus, there are critical points at (0, 0), , and .
Take the second derivative to find any points of inflection.
= 16 − 192x^2This equals zero at x = and x = −.
Next, plug x = and x = − into the original equation to find the y-coordinates of the points of
inflection, which are at and . Now determine whether the points are maxima or
minima.
At x = 0, we have a minimum; the curve is concave up there.
At x = , it’s a maximum, and the curve is concave down.
At x = − , it’s also a maximum (still concave down).
Now plot.