Answer:
roots at -4, 2, 6
Explanation:
This appears to be a cubic polynomial since it has a local maximum and a minimum... Also there are 3 roots.
f(x) = a*(x + 4)*(x - 2)*(x - 6)
with f(0) = 1 = a*(4)*(-2)*(-6)
1 = a * 48
a = (1/48)
f(x) = (1/48)*(x + 4)*(x - 2)*(x - 6)
f '(x) = (1/48) (x - 2)(x - 6) + (1/48)*(x + 4) [ (x - 6) + (x - 2) ]
f '(x) = (1/48) (x - 2)(x - 6) + (1/48)*(x + 4) [ 2x - 8 ]
...
f(x) = (1/48)*(x + 4)*(x - 2)*(x - 6)
roots at -4, 2, 6