Calculus (derivatives)

Question

Calculus derivative help

https://docs.google.com/document/d/1UfT3mFkkl48xP202eFL9o0CRVIq_YedMSSRpH5ztvX0/edit?usp=sharing

(It wont let me add images so everything is in this google doc!)

Answer 1

Thanks for sending the link.

The first graph (the cubic) is x³ - 9x (roots of 3, -3 and 0); therefore, the derivative is 3x² - 9 and evaluated at x=0 is -9. The graph doesn't make it look that steep, but it is.

The second graph is apparently a quartic with a double root at 0, i.e. x⁴ - 9x² which obviously has derivative 0 at x=0.