3. Given f(x) = 1 /2 x ^4 and g(x) = |x^ 2 − 14|:

Question

(a) Plot the two functions on the same axes with x-interval [−4, 4].

(b) Find the points of intersection (approximate if necessary).

(c) Find the volume of the solid whose base is the region enclosed by the two curves, and

whose cross-sections are square-shaped and perpendicular to the x-axis (approximate if

necessary).

Answer 1

desmos.com/calculator/vffoob5edy

desmos.com/3d/1menq1iszu

Answer 2

I have provided a detailed walkthrough of each part of this question at: https://ianvb.notion.site/graphing-intersections-volume. In addition to guidance on this specific question, you should find some generally useful Python and plotting tricks there too. Let me know if you have any questions!