Question

Write a formula for a function with x intercepts at -3, 3, and 4. How many local maxima or minima does it have

Answer 1

The minimal polynomial that satisfies this would be something like \((x+3)(x-3)(x-4)\), but that's not to say you can't have something like \(\bigg((x+3)(x-3)(x-4)\bigg)^2\), which would change the number of extrema...

Answer 2

Thanks so much. That's basically what I came up with after reading and reading
y=(x+3)(x-3)(x+4)