PROBLEM 2. Sketch the graph of y = 8x^2 − 16x^4 . Plot all extrema, points of inflection, and asymptotes.
Answer: Factor the polynomial.
8 x^2 (1 − 2x^2 ) = 0Solving for x, we get x = 0 (a double root), x = , and x = −.
Find the y-intercepts: when x = 0, y = 0.
There are no asymptotes, because the curve is a simple polynomial.
Find the critical points using the first derivative.
= 16x − 64x^3Set the derivative equal to zero and solve for x. You get x = 0, x = , and x = −.
Next, plug x = 0, x = , and x = − into the original equation to find the y-coordinates of the critical
points.